1534:± 0.005 kg measurement uncertainty may be implied. If the mass of an object is estimated as 3.78 ± 0.07 kg, so the actual mass is probably somewhere in the range 3.71 to 3.85 kg, and it is desired to report it with a single number, then 3.8 kg is the best number to report since its implied uncertainty ± 0.05 kg gives a mass range of 3.75 to 3.85 kg, which is close to the measurement range. If the uncertainty is a bit larger, i.e. 3.78 ± 0.09 kg, then 3.8 kg is still the best single number to quote, since if "4 kg" was reported then a lot of information would be lost.
162:
396:
50:
1846:
significant figure in each factor is irrelevant. For addition and subtraction, only the digit position of the last significant figure in each of the terms in the calculation matters; the total number of significant figures in each term is irrelevant. However, greater accuracy will often be obtained if some non-significant digits are maintained in intermediate results which are used in subsequent calculations.
313:. For instance, 013 kg has two significant figures—1 and 3—while the leading zero is insignificant since it does not impact the mass indication; 013 kg is equivalent to 13 kg, rendering the zero unnecessary. Similarly, in the case of 0.056 m, there are two insignificant leading zeros since 0.056 m is the same as 56 mm, thus the leading zeros do not contribute to the length indication.
454:
2285:
2447:"accuracy" is actually used in the scientific community, there is a recent standard, ISO 5725, which keeps the same definition of precision but defines the term "trueness" as the closeness of a given measurement to its true value and uses the term "accuracy" as the combination of trueness and precision. (See the
939:, which rounds to the nearest even number. With this method, 1.25 is rounded down to 1.2. If this method applies to 1.35, then it is rounded up to 1.4. This is the method preferred by many scientific disciplines, because, for example, it avoids skewing the average value of a long list of values upwards.
2379:
When performing multiple stage calculations, do not round intermediate stage calculation results; keep as many digits as is practical (at least one more digit than the rounding rule allows per stage) until the end of all the calculations to avoid cumulative rounding errors while tracking or recording
573:
45,600 has 3, 4 or 5 significant figures depending on how the last zeros are used. For example, if the length of a road is reported as 45600 m without information about the reporting or measurement resolution, then it is not clear if the road length is precisely measured as 45600 m or if it
302:
Another example involves a volume measurement of 2.98 L with an uncertainty of ± 0.05 L. The actual volume falls between 2.93 L and 3.03 L. Even if certain digits are not completely known, they are still significant if they are meaningful, as they indicate the actual volume within
896:
digits, since it handles numbers of different scales in a uniform way. For example, the population of a city might only be known to the nearest thousand and be stated as 52,000, while the population of a country might only be known to the nearest million and be stated as 52,000,000. The former might
319:
when they serve as placeholders. In the measurement 1500 m, when the measurement resolution is 100 m, the trailing zeros are insignificant as they simply stand for the tens and ones places. In this instance, 1500 m indicates the length is approximately 1500 m rather than an exact
2416:
It is also possible that the overall length of a ruler may not be accurate to the degree of the smallest mark, and the marks may be imperfectly spaced within each unit. However assuming a normal good quality ruler, it should be possible to estimate tenths between the nearest two marks to achieve an
754:
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if the number 1300 is precise to the nearest unit (just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundreds
461:
Identifying the significant figures in a number requires knowing which digits are meaningful, which requires knowing the resolution with which the number is measured, obtained, or processed. For example, if the measurable smallest mass is 0.001 g, then in a measurement given as 0.00234 g
298:
For instance, if a length measurement yields 114.8 mm, using a ruler with the smallest interval between marks at 1 mm, the first three digits (1, 1, and 4, representing 114 mm) are certain and constitute significant figures. Further, digits that are uncertain yet meaningful are
1736:
For unit conversion, the implied uncertainty of the result can be unsatisfactorily higher than that in the previous unit if this rounding guideline is followed; For example, 8 inch has the implied uncertainty of ± 0.5 inch = ± 1.27 cm. If it is converted to the centimeter
1727:
significant figures respectively. (2 here is assumed not an exact number.) For the first example, the first multiplication factor has four significant figures and the second has one significant figure. The factor with the fewest or least significant figures is the second one with only one, so the
1664:
The guidelines described below are intended to avoid a calculation result more precise than the measured quantities, but it does not ensure the resulted implied uncertainty close enough to the measured uncertainties. This problem can be seen in unit conversion. If the guidelines give the implied
611:
is irrational — not all of the digits are known. As of March 2024, more than 102 trillion digits have been calculated. A 102 trillion-digit approximation has 102 trillion significant digits. In practical applications, far fewer digits are used. The everyday approximation 3.14 has
2412:
When using a ruler, initially use the smallest mark as the first estimated digit. For example, if a ruler's smallest mark is 0.1 cm, and 4.5 cm is read, then it is 4.5 (±0.1 cm) or 4.4 cm to 4.6 cm as to the smallest mark interval. However, in practice a measurement can
1533:
Uncertainty may be implied by the last significant figure if it is not explicitly expressed. The implied uncertainty is ± the half of the minimum scale at the last significant figure position. For example, if the mass of an object is reported as 3.78 kg without mentioning uncertainty, then
2446:
Traditionally, in various technical fields, "accuracy" refers to the closeness of a given measurement to its true value; "precision" refers to the stability of that measurement when repeated many times. Thus, it is possible to be "precisely wrong". Hoping to reflect the way in which the term
1845:
The rule to calculate significant figures for multiplication and division are not the same as the rule for addition and subtraction. For multiplication and division, only the total number of significant figures in each of the factors in the calculation matters; the digit position of the last
354:
to present a measurement as 12.34525 kg when the measuring instrument only provides accuracy to the nearest gram (0.001 kg). In this case, the significant figures are the first five digits (1, 2, 3, 4, and 5) from the leftmost digit, and the number should be rounded to these
2380:
the significant figures in each intermediate result. Then, round the final result, for example, to the fewest number of significant figures (for multiplication or division) or leftmost last significant digit position (for addition or subtraction) among the inputs in the final calculation.
1754:
6 ≈ 11.11. However, this multiplication is essentially adding 1.234 to itself 9 times such as 1.234 + 1.234 + … + 1.234 so the rounding guideline for addition and subtraction described below is more proper rounding approach. As a result, the final answer is 1.234 + 1.234 + … + 1.234 =
290:
that carry both reliability and necessity in conveying a particular quantity. When presenting the outcome of a measurement (such as length, pressure, volume, or mass), if the number of digits exceeds what the measurement instrument can resolve, only the number of digits within the
897:
be in error by hundreds, and the latter might be in error by hundreds of thousands, but both have two significant figures (5 and 2). This reflects the fact that the significance of the error is the same in both cases, relative to the size of the quantity being measured.
588:
If the number of apples in a bag is 4 (exact number), then this number is 4.0000... (with infinite trailing zeros to the right of the decimal point). As a result, 4 does not impact the number of significant figures or digits in the result of calculations with
1581:
are the number with an extra zero digit (to follow the rules to write uncertainty above) and the implied uncertainty of it respectively. For example, 6 kg with the implied uncertainty ± 0.5 kg can be stated as 6.0 ± 0.5 kg.
616:
digits. The approximation 22/7 has the same three correct decimal digits but has 10 correct binary digits. Most calculators and computer programs can handle the 16-digit expansion 3.141592653589793, which is sufficient for interplanetary navigation
342:
is the one with the lowest exponent value (the rightmost significant digit/figure). For example, in the number "123" the "1" is the most significant digit, representing hundreds (10), while the "3" is the least significant digit, representing ones (10).
2555:
mode in which the calculator will evaluate the count of significant digits of entered numbers and display it in square brackets behind the corresponding number. The results of calculations will be adjusted to only show the significant digits as well.
359:(in this example, 0.00025 kg = 0.25 g) approximates the numerical resolution or precision. Numbers can also be rounded for simplicity, not necessarily to indicate measurement precision, such as for the sake of expediency in news broadcasts.
2013:
1634:) has no effect on the determination of the significant figures in the result of a calculation with it if its known digits are equal to or more than the significant figures in the measured quantities used in the calculation. An exact number such as
2431:
When estimating the proportion of individuals carrying some particular characteristic in a population, from a random sample of that population, the number of significant figures should not exceed the maximum precision allowed by that sample size.
574:
is a rough estimate. If it is the rough estimation, then only the first three non-zero digits are significant since the trailing zeros are neither reliable nor necessary; 45600 m can be expressed as 45.6 km or as 4.56 × 10 m in
526:
If a length measurement gives 0.052 km, then 0.052 km = 52 m so 5 and 2 are only significant; the leading zeros appear or disappear, depending on which unit is used, so they are not necessary to indicate the measurement
330:
A zero after a decimal (e.g., 1.0) is significant, and care should be used when appending such a decimal of zero. Thus, in the case of 1.0, there are two significant figures, whereas 1 (without a decimal) has one significant figure.
299:
also included in the significant figures. In this example, the last digit (8, contributing 0.8 mm) is likewise considered significant despite its uncertainty. Therefore, this measurement contains four significant figures.
606:
with several equivalent definitions. All of the digits in its exact decimal expansion 3.14159265358979323... are significant. Although many properties of these digits are known — for example, they do not repeat, because
1262:
479:
123.45 has five significant digits (1, 2, 3, 4 and 5) if they are within the measurement resolution. If the resolution is, say, 0.1, then the 5 shows that the true value to 4 sig figs is equally likely to be 123.4 or
303:
an acceptable range of uncertainty. In this case, the actual volume might be 2.94 L or possibly 3.02 L, so all three digits are considered significant. Thus, there are three significant figures in this example.
2365:
741:
677:
1836:
place respectively. (2 here is assumed not an exact number.) For the first example, the first term has its last significant figure in the thousandths place and the second term has its last significant figure in the
948:
digit with zeros. For example, if 1254 is rounded to 2 significant figures, then 5 and 4 are replaced to 0 so that it will be 1300. For a number with the decimal point in rounding, remove the digits after the
1741:
0.32 cm ≈ 20 cm with the implied uncertainty of ± 5 cm. If this implied uncertainty is considered as too overestimated, then more proper significant digits in the unit conversion result may be
1749:
Another exception of applying the above rounding guideline is to multiply a number by an integer, such as 1.234 × 9. If the above guideline is followed, then the result is rounded as 1.234 × 9.000.... =
1841:
place. The leftmost or largest digit position among the last significant figures of these terms is the ones place, so the calculated result should also have its last significant figure in the ones place.
1339:
755:
due to rounding or uncertainty. Many conventions exist to address this issue. However, these are not universally used and would only be effective if the reader is familiar with the convention:
1910:
When taking the antilogarithm of a normalized number, the result is rounded to have as many significant figures as the significant figures in the decimal part of the number to be antiloged.
2962:
1485:
1408:
819:. For example, the precision of measurement specified as 1300 g is ambiguous, while if stated as 1.30 kg it is not. Likewise 0.0123 L can be rewritten as 12.3 mL.
2280:{\displaystyle {\rm {(significant~figures~of~f(x))}}\approx {\rm {(significant~figures~of~x)}}-\log _{10}\left(\left\vert {{\frac {df(x)}{dx}}{\frac {x}{f(x)}}}\right\vert \right)}
1519:
are the same, otherwise the consistency is lost. For example, "1.79 ± 0.067" is incorrect, as it does not make sense to have more accurate uncertainty than the best estimate.
3132:
2413:
usually be estimated by eye to closer than the interval between the ruler's smallest mark, e.g. in the above case it might be estimated as between 4.51 cm and 4.53 cm.
1568:
326:
digits that arise from calculations resulting in a higher precision than the original data or a measurement reported with greater precision than the instrument's resolution.
805:
As the conventions above are not in general use, the following more widely recognized options are available for indicating the significance of number with trailing zeros:
961:
for many world currencies. This is done because greater precision is immaterial, and usually it is not possible to settle a debt of less than the smallest currency unit.
979:
in some manner to fit the available precision. The following table shows the results for various total precision at two rounding ways (N/A stands for Not
Applicable).
865:
Explicitly state the number of significant figures (the abbreviation s.f. is sometimes used): For example "20 000 to 2 s.f." or "20 000 (2 sf)".
1998:
1957:
362:
Significance arithmetic encompasses a set of approximate rules for preserving significance through calculations. More advanced scientific rules are known as the
2469:
Computer representations of floating-point numbers use a form of rounding to significant figures (while usually not keeping track of how many), in general with
1775:, the last significant figure position (e.g., hundreds, tens, ones, tenths, hundredths, and so forth) in the calculated result should be the same as the
933:(also known as "5/4") rounds up to 1.3. This is the default rounding method implied in many disciplines if the required rounding method is not specified.
1206:
2791:
3121:"Solution 30190: Using The Significant Numbers Calculator From The Science Tools App on the TI-83 Plus and TI-84 Plus Family of Graphing Calculators"
2737:
2293:
2973:
682:
2498:
2494:
627:
3221:
1661:
has no bearing on the significant figures in the calculated kinetic energy since its number of significant figures is infinite (0.500000...).
555:
120.000 consists of six significant figures (1, 2, and the four subsequent zeroes) if, as before, they are within the measurement resolution.
799:
A decimal point may be placed after the number; for example "1300." indicates specifically that trailing zeros are meant to be significant.
975:
can be expressed with various numbers of significant figures or decimal places. If insufficient precision is available then the number is
3098:
3120:
2417:
extra decimal place of accuracy. Failing to do this adds the error in reading the ruler to any error in the calibration of the ruler.
258:
2876:
953:
digit. For example, if 14.895 is rounded to 3 significant figures, then the digits after 8 are removed so that it will be 14.9.
828:
Eliminate ambiguous or non-significant zeros by using
Scientific Notation: For example, 1300 with three significant figures becomes
3345:– Proper methods for expressing uncertainty, including a detailed discussion of the problems with any notion of significant digits.
118:
2990:
1665:
uncertainty too far from the measured ones, then it may be needed to decide significant digits that give comparable uncertainty.
90:
3064:
3192:
3162:
1497:
should usually be quoted to only one or two significant figures, as more precision is unlikely to be reliable or meaningful:
964:
In UK personal tax returns, income is rounded down to the nearest pound, whilst tax paid is calculated to the nearest penny.
1271:
413:
97:
71:
1971:) is differentiable at its domain element 'x', then its number of significant figures (denoted as "significant figures of
1570:
with stating it as the implied uncertainty (to prevent readers from recognizing it as the measurement uncertainty), where
2767:
462:
the "4" is not useful and should be discarded, while the "3" is useful and should often be retained.
2890:
957:
In financial calculations, a number is often rounded to a given number of places. For example, to two places after the
17:
769:, may be placed over the last significant figure; any trailing zeros following this are insignificant. For example, 13
3010:
As a general rule you should attempt to read any scale to one tenth of its smallest division by visual interpolation.
2843:
435:
137:
104:
3095:
3060:
3310:
E29-06b, Standard
Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications
86:
417:
75:
2734:
Giving a precise definition for the number of correct significant digits is not a straightforward matter: see
878:, as in 20 000 ± 1%. This also allows specifying a range of precision in-between powers of ten.
3320:
1441:
1364:
251:
2802:
552:
0.0980 has three significant digits (9, 8, and the last zero) if they are within the measurement resolution.
67:
2673:
549:
1.200 has four significant figures (1, 2, 0, and 0) if they are allowed by the measurement resolution.
181:
2451:
article for a full discussion.) In either case, the number of significant figures roughly corresponds to
3363:
2491:
916:
digit. For example, if we want to round 1.2459 to 3 significant figures, then this step results in 1.25.
363:
31:
1540:
844:. The part of the representation that contains the significant figures (1.30 or 1.23) is known as the
504:
125.340006 has seven significant figures if the resolution is to 0.0001: 1, 2, 5, 3, 4, 0, and 0.
2668:
2464:
1594:
quantities, there are also guidelines (not rules) to determine the significant figures in quantities
773:
0 has three significant figures (and hence indicates that the number is precise to the nearest ten).
3214:
1685:
number of significant figures among the measured quantities used in the calculation. For example,
244:
2755:
2477:(which has the advantage of being a more accurate measure of precision, and is independent of the
1928:
406:
111:
60:
2972:. California Institute of Technology, Physics Mathematics And Astronomy Division. Archived from
923:+ 1 digit is 5 not followed by other digits or followed by only zeros, then rounding requires a
3028:
2860:
2448:
2441:
1968:
782:
Less often, using a closely related convention, the last significant figure of a number may be
376:
338:
is the one with the greatest exponent value (the leftmost significant digit/figure), while the
292:
176:
3089:
3333:
and some explanations of the shortcomings of significance arithmetic and significant figures.
2911:
2835:
2828:
2484:
1855:
1438:
can be the standard deviation or a multiple of the measurement deviation. The rules to write
930:
38:
2637:
2548:
1960:
1879:
1537:
If there is a need to write the implied uncertainty of a number, then it can be written as
232:
222:
1974:
1933:
1361:
It is recommended for a measurement result to include the measurement uncertainty such as
8:
3358:
2870:
2663:
2474:
875:
816:
575:
287:
3296:
3267:
1882:) has as many significant figures as the significant figures in the normalized number.
856:) are considered exact numbers so for these digits, significant figures are irrelevant.
749:
3325:
3022:
936:
27:
Any digit of a number within its measurement resolution, as opposed to spurious digits
3128:
2998:
2929:
2839:
2537:
1863:
958:
766:
476:
91 has two significant figures (9 and 1) if they are measurement-allowed digits.
161:
912:+ 1 digit is greater than 5 or is 5 followed by other non-zero digits, add 1 to the
3288:
3259:
3051:
2631:
2618:
2614:
2606:
2368:
1737:
scale and the rounding guideline for multiplication and division is followed, then
3279:
Bond, E. A. (1931). "Significant Digits in
Computation with Approximate Numbers".
3184:
3154:
1257:{\displaystyle 10^{n}\cdot \operatorname {round} \left({\frac {x}{10^{n}}}\right)}
3326:
The
Decimal Arithmetic FAQ — Is the decimal arithmetic ‘significance’ arithmetic?
2678:
2647:
2560:
1522:
1.79 ± 0.06 (correct), 1.79 ± 0.96 (correct), 1.79 ± 0.067 (incorrect).
621:
351:
283:
196:
2473:. The number of correct significant figures is closely related to the notion of
1500:
1.79 ± 0.06 (correct), 1.79 ± 0.96 (correct), 1.79 ± 1.96 (incorrect).
924:
595:
A mathematical or physical constant has significant figures to its known digits.
501:
101.12003 consists of eight significant figures if the resolution is to 0.00001.
3343:
Measurements and
Uncertainties versus Significant Digits or Significant Figures
1639:
1618:
356:
186:
3342:
3330:
3155:"Bit's WP 34S and 31S patches and custom binaries (version: r3802 20150805-1)"
1746:.32 cm ≈ 20. cm with the implied uncertainty of ± 0.5 cm.
530:
0.00034 has 2 significant figures (3 and 4) if the resolution is 0.00001.
3352:
2943:
2487:
supporting a dedicated significant figures display mode are relatively rare.
2470:
2360:{\displaystyle \left\vert {{\frac {df(x)}{dx}}{\frac {x}{f(x)}}}\right\vert }
1609:
quantities are most important in the determination of significant figures in
613:
537:
316:
227:
217:
191:
2705:
892:
to significant figures is a more general-purpose technique than rounding to
736:{\displaystyle h=6.62607015(0)\times 10^{-34}\mathrm {J} \cdot \mathrm {s} }
355:
significant figures, resulting in 12.345 kg as the accurate value. The
323:
2599:
1898:(3.000) = 4.000000... (exact number so infinite significant digits) + 0.477
513:
310:
3336:
3292:
3263:
2652:
2603:
845:
812:
672:{\displaystyle h=6.62607015\times 10^{-34}\mathrm {J} \cdot \mathrm {s} }
603:
3300:
3271:
2435:
679:
and is defined as an exact value so that it is more properly defined as
2544:
2540:
2426:
1681:, the calculated result should have as many significant figures as the
1424:
are the best estimate and uncertainty in the measurement respectively.
1200:
significant digits has a numerical value that is given by the formula:
420: in this section. Unsourced material may be challenged and removed.
2000:") is approximately related with the number of significant figures in
346:
To avoid conveying a misleading level of precision, numbers are often
2642:
1964:
1859:
783:
457:
Digits in light blue are significant figures; those in black are not.
1779:
or largest digit position among the last significant figures of the
1590:
As there are rules to determine the significant figures in directly
750:
Ways to denote significant figures in an integer with trailing zeros
467:
Non-zero digits within the given measurement or reporting resolution
448:
395:
49:
2657:
976:
889:
762:
347:
295:'s capability are dependable and therefore considered significant.
3339:– Displays a number with the desired number of significant digits.
3185:"[34S & 31S] Unique display mode: significant figures"
1762:
1728:
final calculated result should also have one significant figure.
1344:
which may need to be written with a specific marking as detailed
968:
927:
rule. For example, to round 1.25 to 2 significant figures:
3250:
Delury, D. B. (1958). "Computations with approximate numbers".
2610:
2575:
2571:
2567:
2563:
3027:. Newark, NJ: Weston Electrical Instruments Co. 1914. p.
1878:
as an integer), is rounded such that its decimal part (called
1351:
584:
An exact number has an infinite number of significant figures.
306:
The following types of digits are not considered significant:
2826:
Myers, R. Thomas; Oldham, Keith B.; Tocci, Salvatore (2000).
2478:
2374:
1356:
874:
State the expected variability (precision) explicitly with a
811:
Eliminate ambiguous or non-significant zeros by changing the
372:
10 (base-10, decimal numbers) is assumed in the following. (S
369:
2819:
546:
if they are within the measurement or reporting resolution.
3307:
2621:(2023) support a significant figures display mode as well.
2877:
Numerical
Mathematics and Computing, by Cheney and Kincaid
2490:
Among the calculators to support related features are the
765:, sometimes also called an overbar, or less accurately, a
453:
1082:. (Remember that the leading zeros are not significant.)
944:
For an integer in rounding, replace the digits after the
1345:
570:, depending on the measurement or reporting resolution.
2916:
Purdue
University - Department of Physics and Astronomy
2768:"How Many Decimals of Pi Do We Really Need? - Edu News"
1505:
The digit positions of the last significant figures in
2481:, also known as the base, of the number system used).
1613:
with them. A mathematical or physical constant (e.g.,
2960:
2578:(2014) calculators significant figures display modes
2455:, not to accuracy or the newer concept of trueness.
2436:
Relationship to accuracy and precision in measurement
2296:
2016:
1977:
1936:
1543:
1444:
1367:
1348:
to specify the number of significant trailing zeros.
1334:{\displaystyle n=\lfloor \log _{10}(|x|)\rfloor +1-p}
1274:
1209:
685:
630:
578:, and neither expression requires the trailing zeros.
37:"First digit" redirects here. For the body part, see
2861:"Rounding Decimal Numbers to a Designated Precision"
1767:
For quantities created from measured quantities via
1673:
For quantities created from measured quantities via
78:. Unsourced material may be challenged and removed.
2858:
2827:
2359:
2279:
1992:
1951:
1562:
1479:
1402:
1333:
1256:
884:
848:or mantissa. The digits in the base and exponent (
735:
671:
385:
3063:/ Mitchells Printers (Luton) Limited. 201318-01.
2944:"Uncertainty in Measurement- Significant Figures"
2866:. Washington, D.C.: U.S. Department of Education.
449:Rules to identify significant figures in a number
3350:
2834:. Austin, Texas: Holt Rinehart Winston. p.
2825:
2501:(1976), which support two display modes, where
1763:Addition and subtraction of significant figures
536:Zeros to the right of the last non-zero digit (
2983:
2963:"Measurements and Significant Figures (Draft)"
2739:Accuracy and Stability of Numerical Algorithms
1849:
1668:
3082:
3044:
1783:quantities in the calculation. For example,
612:three significant figures and 7 correct
510:Zeros to the left of the first non-zero digit
486:Zeros between two significant non-zero digits
252:
3206:
2407:
1316:
1281:
380:for extending these concepts to other bases.
1922:
1759:= 11.106 (one significant digit increase).
1352:Writing uncertainty and implied uncertainty
3091:commodore s61 Statistician Owners Handbook
3059:. Palo Alto, California, USA / Luton, UK:
2420:
2375:Round only on the final calculation result
1431:can be the average of measured values and
1357:Significant figures in writing uncertainty
259:
245:
3331:Advanced methods for handling uncertainty
3321:Significant Figures Video by Khan academy
3053:commodore m55 Mathematician Owners Manual
1820:with the last significant figures in the
436:Learn how and when to remove this message
334:Among a number's significant digits, the
138:Learn how and when to remove this message
3176:
3146:
2997:. University of Michigan. Archived from
2961:de Oliveira Sannibale, Virgínio (2001).
2859:Engelbrecht, Nancy; et al. (1990).
1192:The representation of a non-zero number
452:
66:Relevant discussion may be found on the
3212:
3113:
2891:"Uncertainties and Significant Figures"
2760:
2609:-based community-developed calculators
2598:(with zero padding) are available as a
1480:{\displaystyle x_{best}\pm \sigma _{x}}
1403:{\displaystyle x_{best}\pm \sigma _{x}}
14:
3351:
3249:
3015:
2735:
1528:
836:. Likewise 0.0123 can be rewritten as
3215:"Changes from the WP43S to the WP43C"
3213:Mostert, Jaco "Jaymos" (2020-02-11).
2703:
3278:
3189:MoHPC - The Museum of HP Calculators
3159:MoHPC - The Museum of HP Calculators
2699:
2697:
2695:
2004:(denoted as "significant figures of
540:) in a number with the decimal point
418:adding citations to reliable sources
389:
76:adding citations to reliable sources
43:
3182:
3152:
2745:(2nd ed.). SIAM. pp. 3–5.
2515:significant digits in total, while
24:
3243:
2706:"Significant Figures and Rounding"
2185:
2179:
2176:
2170:
2167:
2164:
2161:
2158:
2155:
2152:
2146:
2143:
2140:
2137:
2134:
2131:
2128:
2125:
2122:
2119:
2116:
2097:
2091:
2085:
2082:
2076:
2073:
2070:
2067:
2064:
2061:
2058:
2052:
2049:
2046:
2043:
2040:
2037:
2034:
2031:
2028:
2025:
2022:
1918:8.5318119... = 30000 = 3.000 × 10.
729:
721:
665:
657:
25:
3375:
3314:
3039:Experimental Electrical Testing..
2692:
3096:Commodore Business Machines Inc.
3061:Commodore Business Machines Inc.
2888:
1563:{\displaystyle x\pm \sigma _{x}}
1182:
1068:
790:00" has two significant figures.
394:
350:. For instance, it would create
160:
48:
3227:from the original on 2023-10-01
3195:from the original on 2023-09-24
3165:from the original on 2023-09-24
3135:from the original on 2023-09-16
3101:from the original on 2023-09-30
3070:from the original on 2023-09-30
3024:Experimental Electrical Testing
2954:
2936:
2922:
2904:
2882:
2725:; Kendall-Hunt:Dubuque, IA 1988
2458:
885:Rounding to significant figures
405:needs additional citations for
386:Identifying significant figures
59:needs additional citations for
3337:Significant Figures Calculator
3094:. Palo Alto, California, USA:
2852:
2792:"Resolutions of the 26th CGPM"
2784:
2749:
2728:
2716:
2660:(IEEE floating-point standard)
2346:
2340:
2317:
2311:
2262:
2256:
2233:
2227:
2188:
2113:
2103:
2100:
2094:
2019:
1987:
1981:
1946:
1940:
1313:
1309:
1301:
1297:
701:
695:
13:
1:
2704:Lower, Stephen (2021-03-31).
2685:
2395:(2.3494 × 1.345) + 1.2 = 3.15
2384:(2.3494 + 1.345) × 1.2 = 3.69
1585:
2801:. 2018-11-16. Archived from
2756:"y-cruncher validation file"
2674:Precision (computer science)
1731:
561:Trailing zeros in an integer
7:
2970:Freshman Physics Laboratory
2624:
2570:-based community-developed
1850:Logarithm and antilogarithm
1669:Multiplication and division
286:within a number written in
10:
3380:
2930:"Significant Figure Rules"
2723:Chemistry in the Community
2462:
2439:
2424:
364:propagation of uncertainty
36:
32:Significant Figures (book)
29:
2736:Higham, Nicholas (2002).
2669:Kahan summation algorithm
2465:Floating-point arithmetic
2408:Estimating an extra digit
931:Round half away from zero
2932:. Penn State University.
1923:Transcendental functions
967:As an illustration, the
30:Not to be confused with
3281:The Mathematics Teacher
3252:The Mathematics Teacher
2421:Estimation in statistic
1969:trigonometric functions
1929:transcendental function
1638:in the formula for the
1617:in the formula for the
1605:Significant figures in
340:least significant digit
177:Orders of approximation
2948:Chemistry - LibreTexts
2710:Chemistry - LibreTexts
2485:Electronic calculators
2449:accuracy and precision
2442:Accuracy and precision
2361:
2281:
1994:
1953:
1564:
1481:
1404:
1335:
1258:
737:
673:
458:
377:unit in the last place
336:most significant digit
274:, also referred to as
2912:"Significant Figures"
2549:graphical calculators
2362:
2282:
1995:
1954:
1611:calculated quantities
1565:
1482:
1405:
1336:
1259:
904:significant figures:
900:To round a number to
738:
674:
456:
320:value of 1500 m.
87:"Significant figures"
39:First digit (anatomy)
3293:10.5951/MT.24.4.0208
3264:10.5951/MT.51.7.0521
2638:Engineering notation
2294:
2014:
1993:{\displaystyle f(x)}
1975:
1961:exponential function
1952:{\displaystyle f(x)}
1934:
1541:
1442:
1365:
1272:
1207:
1078:Another example for
683:
628:
414:improve this article
233:Scientific modelling
223:Generalization error
72:improve this article
2664:Interval arithmetic
2547:(2004) families of
1529:Implied uncertainty
1139:0.01234 or 0.01235
1131:0.01234 or 0.01235
1093:significant figures
990:significant figures
817:unit of measurement
815:in a number with a
576:scientific notation
288:positional notation
272:Significant figures
202:Significant figures
3364:Numerical analysis
3183:Bit (2015-02-07).
3153:Bit (2014-11-15).
2553:Sig-Fig Calculator
2357:
2277:
2008:") by the formula
1990:
1949:
1890:(3.000 × 10) = log
1560:
1477:
1400:
1331:
1254:
1196:to a precision of
937:Round half to even
733:
669:
459:
276:significant digits
210:Other fundamentals
18:Significant figure
3129:Texas Instruments
2995:slc.umd.umich.edu
2634:(first-digit law)
2538:Texas Instruments
2495:M55 Mathematician
2350:
2329:
2266:
2245:
2184:
2175:
2151:
2090:
2081:
2057:
1902:212547... = 4.477
1864:normalized number
1705:0.01234 × 2 = 0.0
1248:
1190:
1189:
1076:
1075:
959:decimal separator
786:; for example, "1
446:
445:
438:
269:
268:
228:Taylor polynomial
155:Fit approximation
148:
147:
140:
122:
16:(Redirected from
3371:
3304:
3275:
3237:
3235:
3233:
3232:
3226:
3219:
3210:
3204:
3203:
3201:
3200:
3180:
3174:
3173:
3171:
3170:
3150:
3144:
3143:
3141:
3140:
3117:
3111:
3109:
3107:
3106:
3086:
3080:
3078:
3076:
3075:
3069:
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3041:
3036:
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3019:
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2987:
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2967:
2958:
2952:
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2940:
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2926:
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2823:
2817:
2816:
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2778:
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2758:
2753:
2747:
2746:
2744:
2732:
2726:
2720:
2714:
2713:
2701:
2533:decimal places.
2499:S61 Statistician
2402:
2398:
2391:
2387:
2369:condition number
2366:
2364:
2363:
2358:
2356:
2352:
2351:
2349:
2332:
2330:
2328:
2320:
2303:
2286:
2284:
2283:
2278:
2276:
2272:
2268:
2267:
2265:
2248:
2246:
2244:
2236:
2219:
2205:
2204:
2192:
2191:
2182:
2173:
2149:
2107:
2106:
2088:
2079:
2055:
1999:
1997:
1996:
1991:
1958:
1956:
1955:
1950:
1917:
1906:212547 ≈ 4.4771.
1905:
1901:
1813:
1806:
1799:
1796:1.234 + 2.0 = 3.
1792:
1758:
1753:
1745:
1740:
1708:
1701:
1698:1.234 × 2.0 = 2.
1694:
1660:
1653:
1647:
1637:
1633:
1626:
1619:area of a circle
1616:
1569:
1567:
1566:
1561:
1559:
1558:
1486:
1484:
1483:
1478:
1476:
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1463:
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1409:
1407:
1406:
1401:
1399:
1398:
1386:
1385:
1340:
1338:
1337:
1332:
1312:
1304:
1293:
1292:
1263:
1261:
1260:
1255:
1253:
1249:
1247:
1246:
1234:
1219:
1218:
1085:
1084:
982:
981:
855:
851:
843:
841:
835:
833:
789:
772:
742:
740:
739:
734:
732:
724:
719:
718:
678:
676:
675:
670:
668:
660:
655:
654:
441:
434:
430:
427:
421:
398:
390:
261:
254:
247:
164:
152:
151:
143:
136:
132:
129:
123:
121:
80:
52:
44:
21:
3379:
3378:
3374:
3373:
3372:
3370:
3369:
3368:
3349:
3348:
3317:
3246:
3244:Further reading
3241:
3240:
3230:
3228:
3224:
3217:
3211:
3207:
3198:
3196:
3181:
3177:
3168:
3166:
3151:
3147:
3138:
3136:
3119:
3118:
3114:
3104:
3102:
3088:
3087:
3083:
3079:(1+151+1 pages)
3073:
3071:
3067:
3056:
3050:
3049:
3045:
3033:
3031:
3021:
3020:
3016:
3004:
3002:
2989:
2988:
2984:
2976:
2965:
2959:
2955:
2942:
2941:
2937:
2928:
2927:
2923:
2910:
2909:
2905:
2893:
2889:Luna, Eduardo.
2887:
2883:
2875:
2871:
2863:
2857:
2853:
2846:
2824:
2820:
2811:
2809:
2805:
2794:
2790:
2789:
2785:
2776:
2774:
2766:
2765:
2761:
2754:
2750:
2742:
2733:
2729:
2721:
2717:
2702:
2693:
2688:
2683:
2679:Round-off error
2648:False precision
2627:
2597:
2591:
2587:
2581:
2528:
2522:
2518:
2510:
2504:
2497:(1976) and the
2467:
2461:
2444:
2438:
2429:
2423:
2410:
2400:
2396:
2389:
2385:
2377:
2336:
2331:
2321:
2304:
2302:
2301:
2297:
2295:
2292:
2291:
2252:
2247:
2237:
2220:
2218:
2217:
2213:
2209:
2200:
2196:
2112:
2111:
2018:
2017:
2015:
2012:
2011:
1976:
1973:
1972:
1935:
1932:
1931:
1925:
1915:
1903:
1899:
1897:
1893:
1889:
1852:
1811:
1804:
1797:
1790:
1765:
1756:
1751:
1743:
1738:
1734:
1706:
1699:
1692:
1671:
1655:
1649:
1643:
1635:
1628:
1622:
1614:
1588:
1579:
1554:
1550:
1542:
1539:
1538:
1531:
1517:
1510:
1495:
1471:
1467:
1449:
1445:
1443:
1440:
1439:
1436:
1429:
1422:
1415:
1394:
1390:
1372:
1368:
1366:
1363:
1362:
1359:
1354:
1308:
1300:
1288:
1284:
1273:
1270:
1269:
1242:
1238:
1233:
1229:
1214:
1210:
1208:
1205:
1204:
1098:decimal places
1097:
1092:
1050:12.34 or 12.35
1025:12.34 or 12.35
995:decimal places
994:
989:
887:
876:plus–minus sign
853:
849:
839:
837:
831:
829:
787:
770:
752:
728:
720:
711:
707:
684:
681:
680:
664:
656:
647:
643:
629:
626:
625:
622:Planck constant
451:
442:
431:
425:
422:
411:
399:
388:
352:false precision
282:, are specific
265:
197:False precision
144:
133:
127:
124:
81:
79:
65:
53:
42:
35:
28:
23:
22:
15:
12:
11:
5:
3377:
3367:
3366:
3361:
3347:
3346:
3340:
3334:
3328:
3323:
3316:
3315:External links
3313:
3312:
3311:
3305:
3276:
3245:
3242:
3239:
3238:
3205:
3175:
3145:
3125:Knowledge Base
3112:
3081:
3043:
3014:
2991:"Measurements"
2982:
2979:on 2013-06-18.
2953:
2935:
2921:
2903:
2898:DeAnza College
2881:
2869:
2851:
2844:
2818:
2783:
2759:
2748:
2727:
2715:
2690:
2689:
2687:
2684:
2682:
2681:
2676:
2671:
2666:
2661:
2655:
2650:
2645:
2640:
2635:
2628:
2626:
2623:
2617:(2022) /
2613:(2019) /
2593:
2589:
2583:
2579:
2524:
2520:
2516:
2506:
2502:
2475:relative error
2471:binary numbers
2463:Main article:
2460:
2457:
2440:Main article:
2437:
2434:
2425:Main article:
2422:
2419:
2409:
2406:
2405:
2404:
2399:943 + 1.2 = 4.
2393:
2376:
2373:
2355:
2348:
2345:
2342:
2339:
2335:
2327:
2324:
2319:
2316:
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2110:
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2030:
2027:
2024:
2021:
1989:
1986:
1983:
1980:
1948:
1945:
1942:
1939:
1924:
1921:
1920:
1919:
1908:
1907:
1895:
1891:
1887:
1870:× 10 with 1 ≤
1851:
1848:
1818:
1817:
1816:
1815:
1810:12000 + 77 = 1
1808:
1803:0.01234 + 2 =
1801:
1794:
1764:
1761:
1733:
1730:
1713:
1712:
1711:
1710:
1703:
1696:
1675:multiplication
1670:
1667:
1648:with velocity
1640:kinetic energy
1587:
1584:
1577:
1557:
1553:
1549:
1546:
1530:
1527:
1526:
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1237:
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1177:
1176:
1173:
1170:
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1165:
1162:
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1148:
1144:
1143:
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1129:
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1121:
1118:
1115:
1111:
1110:
1107:
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1100:
1099:
1094:
1089:
1074:
1073:
1070:
1067:
1063:
1062:
1059:
1056:
1052:
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1041:
1040:
1037:
1034:
1030:
1029:
1026:
1023:
1019:
1018:
1015:
1012:
1008:
1007:
1004:
1001:
997:
996:
991:
986:
955:
954:
942:
941:
940:
934:
917:
886:
883:
882:
881:
880:
879:
869:
868:
867:
866:
860:
859:
858:
857:
823:
822:
821:
820:
803:
802:
801:
800:
794:
793:
792:
791:
777:
776:
775:
774:
751:
748:
747:
746:
745:
744:
731:
727:
723:
717:
714:
710:
706:
703:
700:
697:
694:
691:
688:
667:
663:
659:
653:
650:
646:
642:
639:
636:
633:
618:
602:is a specific
592:
591:
590:
581:
580:
579:
568:be significant
558:
557:
556:
553:
550:
538:trailing zeros
533:
532:
531:
528:
507:
506:
505:
502:
495:trapped zeros)
483:
482:
481:
477:
450:
447:
444:
443:
402:
400:
393:
387:
384:
357:rounding error
328:
327:
321:
317:Trailing zeros
314:
267:
266:
264:
263:
256:
249:
241:
238:
237:
236:
235:
230:
225:
220:
212:
211:
207:
206:
205:
204:
199:
194:
189:
187:Big O notation
184:
182:Scale analysis
179:
171:
170:
166:
165:
157:
156:
146:
145:
70:. Please help
56:
54:
47:
26:
9:
6:
4:
3:
2:
3376:
3365:
3362:
3360:
3357:
3356:
3354:
3344:
3341:
3338:
3335:
3332:
3329:
3327:
3324:
3322:
3319:
3318:
3309:
3306:
3302:
3298:
3294:
3290:
3287:(4): 208–12.
3286:
3282:
3277:
3273:
3269:
3265:
3261:
3258:(7): 521–30.
3257:
3253:
3248:
3247:
3223:
3216:
3209:
3194:
3190:
3186:
3179:
3164:
3160:
3156:
3149:
3134:
3130:
3126:
3122:
3116:
3110:(2+114 pages)
3100:
3097:
3093:
3092:
3085:
3066:
3062:
3055:
3054:
3047:
3040:
3030:
3026:
3025:
3018:
3011:
3001:on 2017-07-09
3000:
2996:
2992:
2986:
2975:
2971:
2964:
2957:
2950:. 2017-06-16.
2949:
2945:
2939:
2931:
2925:
2917:
2913:
2907:
2899:
2892:
2885:
2878:
2873:
2862:
2855:
2847:
2845:0-03-052002-9
2841:
2837:
2832:
2831:
2822:
2808:on 2018-11-19
2804:
2800:
2793:
2787:
2773:
2769:
2763:
2757:
2752:
2741:
2740:
2731:
2724:
2719:
2711:
2707:
2700:
2698:
2696:
2691:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2636:
2633:
2632:Benford's law
2630:
2629:
2622:
2620:
2616:
2612:
2608:
2605:
2601:
2596:
2586:
2577:
2573:
2569:
2565:
2562:
2557:
2554:
2550:
2546:
2542:
2539:
2534:
2532:
2527:
2514:
2509:
2500:
2496:
2493:
2488:
2486:
2482:
2480:
2476:
2472:
2466:
2456:
2454:
2450:
2443:
2433:
2428:
2418:
2414:
2403:59943 ≈ 4.4.
2394:
2383:
2382:
2381:
2372:
2370:
2353:
2343:
2337:
2333:
2325:
2322:
2314:
2308:
2305:
2298:
2288:
2273:
2269:
2259:
2253:
2249:
2241:
2238:
2230:
2224:
2221:
2214:
2210:
2206:
2201:
2197:
2193:
2108:
2009:
2007:
2003:
1984:
1978:
1970:
1966:
1962:
1943:
1937:
1930:
1913:
1912:
1911:
1885:
1884:
1883:
1881:
1877:
1873:
1869:
1865:
1861:
1857:
1847:
1843:
1840:
1835:
1831:
1827:
1823:
1809:
1802:
1795:
1788:
1787:
1786:
1785:
1784:
1782:
1778:
1774:
1770:
1760:
1747:
1729:
1726:
1722:
1718:
1704:
1697:
1690:
1689:
1688:
1687:
1686:
1684:
1680:
1676:
1666:
1662:
1659:
1652:
1646:
1641:
1632:
1625:
1620:
1612:
1608:
1603:
1601:
1597:
1593:
1583:
1580:
1573:
1555:
1551:
1547:
1544:
1535:
1521:
1520:
1518:
1511:
1504:
1499:
1498:
1496:
1490:
1489:
1488:
1472:
1468:
1464:
1459:
1456:
1453:
1450:
1446:
1437:
1430:
1423:
1416:
1395:
1391:
1387:
1382:
1379:
1376:
1373:
1369:
1349:
1347:
1328:
1325:
1322:
1319:
1305:
1294:
1289:
1285:
1278:
1275:
1268:
1265:
1250:
1243:
1239:
1235:
1230:
1226:
1223:
1220:
1215:
1211:
1203:
1202:
1201:
1199:
1195:
1185:
1179:
1178:
1174:
1171:
1168:
1167:
1163:
1160:
1157:
1156:
1152:
1149:
1146:
1145:
1141:
1138:
1135:
1134:
1130:
1127:
1124:
1123:
1119:
1116:
1113:
1112:
1108:
1105:
1102:
1101:
1095:
1090:
1087:
1086:
1083:
1081:
1071:
1065:
1064:
1060:
1057:
1054:
1053:
1049:
1046:
1043:
1042:
1038:
1035:
1032:
1031:
1027:
1024:
1021:
1020:
1016:
1013:
1010:
1009:
1005:
1002:
999:
998:
992:
987:
984:
983:
980:
978:
974:
970:
965:
962:
960:
952:
947:
943:
938:
935:
932:
929:
928:
926:
922:
918:
915:
911:
907:
906:
905:
903:
898:
895:
891:
877:
873:
872:
871:
870:
864:
863:
862:
861:
847:
827:
826:
825:
824:
818:
814:
810:
809:
808:
807:
806:
798:
797:
796:
795:
785:
781:
780:
779:
778:
768:
764:
760:
759:
758:
757:
756:
725:
715:
712:
708:
704:
698:
692:
689:
686:
661:
651:
648:
644:
640:
637:
634:
631:
623:
619:
617:calculations.
615:
610:
605:
601:
598:
597:
596:
593:
587:
586:
585:
582:
577:
572:
571:
569:
567:
562:
559:
554:
551:
548:
547:
545:
541:
539:
534:
529:
525:
524:
522:
520:
515:
514:leading zeros
511:
508:
503:
500:
499:
497:
496:
493:
490:significant (
487:
484:
478:
475:
474:
472:
468:
465:
464:
463:
455:
440:
437:
429:
419:
415:
409:
408:
403:This section
401:
397:
392:
391:
383:
381:
378:
375:
371:
367:
365:
360:
358:
353:
349:
344:
341:
337:
332:
325:
322:
318:
315:
312:
311:Leading zeros
309:
308:
307:
304:
300:
296:
294:
289:
285:
281:
277:
273:
262:
257:
255:
250:
248:
243:
242:
240:
239:
234:
231:
229:
226:
224:
221:
219:
218:Approximation
216:
215:
214:
213:
209:
208:
203:
200:
198:
195:
193:
192:Curve fitting
190:
188:
185:
183:
180:
178:
175:
174:
173:
172:
168:
167:
163:
159:
158:
154:
153:
150:
142:
139:
131:
120:
117:
113:
110:
106:
103:
99:
96:
92:
89: –
88:
84:
83:Find sources:
77:
73:
69:
63:
62:
57:This article
55:
51:
46:
45:
40:
33:
19:
3284:
3280:
3255:
3251:
3229:. Retrieved
3208:
3197:. Retrieved
3188:
3178:
3167:. Retrieved
3158:
3148:
3137:. Retrieved
3124:
3115:
3103:. Retrieved
3090:
3084:
3072:. Retrieved
3052:
3046:
3038:
3032:. Retrieved
3023:
3017:
3009:
3003:. Retrieved
2999:the original
2994:
2985:
2974:the original
2969:
2956:
2947:
2938:
2924:
2915:
2906:
2897:
2884:
2872:
2854:
2829:
2821:
2810:. Retrieved
2803:the original
2798:
2786:
2775:. Retrieved
2772:NASA/JPL Edu
2771:
2762:
2751:
2738:
2730:
2722:
2718:
2709:
2602:option. The
2600:compile-time
2594:
2584:
2558:
2552:
2535:
2530:
2525:
2512:
2507:
2489:
2483:
2468:
2459:In computing
2452:
2445:
2430:
2415:
2411:
2392:3328 ≈ 4.4.
2388:4 × 1.2 = 4.
2378:
2289:
2010:
2005:
2001:
1926:
1909:
1875:
1874:< 10 and
1871:
1867:
1853:
1844:
1838:
1833:
1829:
1825:
1821:
1819:
1789:1.234 + 2 =
1780:
1776:
1772:
1768:
1766:
1748:
1735:
1724:
1720:
1716:
1714:
1691:1.234 × 2 =
1682:
1678:
1674:
1672:
1663:
1657:
1650:
1644:
1630:
1623:
1621:with radius
1610:
1606:
1604:
1602:quantities.
1599:
1595:
1591:
1589:
1575:
1571:
1536:
1532:
1513:
1506:
1491:
1432:
1425:
1418:
1411:
1360:
1343:
1197:
1193:
1191:
1079:
1077:
972:
966:
963:
956:
950:
945:
925:tie-breaking
920:
913:
909:
901:
899:
893:
888:
804:
753:
608:
599:
594:
583:
565:
563:
560:
543:
535:
518:
517:
509:
494:
491:
489:
485:
470:
466:
460:
432:
423:
412:Please help
407:verification
404:
379:
373:
368:
361:
345:
339:
335:
333:
329:
305:
301:
297:
279:
275:
271:
270:
201:
149:
134:
125:
115:
108:
101:
94:
82:
61:verification
58:
2653:Guard digit
2611:WP 43C
2604:SwissMicros
2576:WP 31S
2574:(2011) and
2572:WP 34S
2543:(1999) and
1959:(e.g., the
1832:place, and
1814:077 ≈ 12000
1773:subtraction
1598:from these
1106:0.01234500
846:significand
813:unit prefix
604:real number
564:may or may
544:significant
521:significant
492:significant
471:significant
3359:Arithmetic
3353:Categories
3236:(30 pages)
3231:2023-10-01
3199:2023-09-24
3169:2023-09-24
3139:2023-09-30
3105:2023-09-30
3074:2023-09-30
3034:2019-01-14
3005:2017-07-03
2812:2018-11-20
2777:2021-10-25
2686:References
2551:support a
2545:TI-84 Plus
2541:TI-83 Plus
2529:will give
2511:will give
2427:Estimation
1967:, and the
1894:(10) + log
1807:.01234 ≈ 2
1709:468 ≈ 0.02
1642:of a mass
1596:calculated
1586:Arithmetic
1117:0.0123450
1109:0.0123450
1096:Rounded to
1091:Rounded to
1006:12.345000
993:Rounded to
988:Rounded to
784:underlined
693:6.62607015
638:6.62607015
293:resolution
98:newspapers
2830:Chemistry
2643:Error bar
2492:Commodore
2453:precision
2207:
2194:−
2109:≈
1965:logarithm
1860:logarithm
1834:thousands
1732:Exception
1552:σ
1548:±
1469:σ
1465:±
1392:σ
1388:±
1326:−
1317:⌋
1295:
1282:⌊
1227:
1221:⋅
1128:0.012345
1120:0.012345
1088:Precision
1017:12.34500
985:Precision
971:quantity
726:⋅
713:−
705:×
662:⋅
649:−
641:×
128:July 2013
68:talk page
3301:27951340
3272:27955748
3222:Archived
3220:. v047.
3193:Archived
3163:Archived
3133:Archived
3131:. 2023.
3099:Archived
3065:Archived
2658:IEEE 754
2625:See also
2559:For the
1914:10 = 299
1880:mantissa
1800:34 ≈ 3.2
1793:.234 ≈ 3
1781:measured
1777:leftmost
1769:addition
1702:68 ≈ 2.5
1695:.468 ≈ 2
1679:division
1607:measured
1600:measured
1592:measured
1410:, where
1080:0.012345
1028:12.3450
1003:12.3450
890:Rounding
767:vinculum
763:overline
426:May 2021
324:Spurious
280:sig figs
169:Concepts
2367:is the
1866:(i.e.,
1828:place,
1824:place,
1150:0.0123
1142:0.0123
1039:12.345
1014:12.345
977:rounded
969:decimal
919:If the
908:If the
348:rounded
112:scholar
3299:
3270:
2842:
2290:where
2183:
2174:
2150:
2089:
2080:
2056:
1963:, the
1826:tenths
1723:, and
1161:0.012
1153:0.012
973:12.345
614:binary
527:scale.
516:) are
480:123.5.
284:digits
114:
107:
100:
93:
85:
3297:JSTOR
3268:JSTOR
3225:(PDF)
3218:(PDF)
3068:(PDF)
3057:(PDF)
2977:(PDF)
2966:(PDF)
2894:(PDF)
2864:(PDF)
2806:(PDF)
2795:(PDF)
2743:(PDF)
2479:radix
1927:If a
1862:of a
1755:11.10
1715:with
1683:least
1487:are:
1346:above
1266:where
1224:round
1172:0.01
1164:0.01
1061:12.3
1036:12.3
370:Radix
119:JSTOR
105:books
3308:ASTM
2840:ISBN
2799:BIPM
2607:DM42
2590:SIG0
2588:and
2536:The
2517:DISP
2503:DISP
1858:-10
1856:base
1854:The
1839:ones
1830:ones
1822:ones
1771:and
1750:11.1
1677:and
1574:and
1512:and
1509:best
1428:best
1417:and
1414:best
1175:0.0
838:1.23
830:1.30
620:The
542:are
488:are
469:are
91:news
3289:doi
3260:doi
2619:C47
2615:C43
2580:SIG
2568:30b
2564:20b
2198:log
1886:log
1725:one
1721:two
1717:one
1654:as
1627:as
1286:log
1072:12
1047:12
852:or
761:An
624:is
589:it.
566:not
519:not
416:by
278:or
74:by
3355::
3295:.
3285:24
3283:.
3266:.
3256:51
3254:.
3191:.
3187:.
3161:.
3157:.
3127:.
3123:.
3037:.
3008:.
2993:.
2968:.
2946:.
2914:.
2896:.
2838:.
2836:59
2797:.
2770:.
2708:.
2694:^
2561:HP
2371:.
2287:,
2202:10
1896:10
1892:10
1888:10
1719:,
1658:mv
1290:10
1240:10
1212:10
1186:0
1169:1
1158:2
1147:3
1136:4
1125:5
1114:6
1103:7
1058:10
1044:2
1033:3
1022:4
1011:5
1000:6
854:10
850:10
842:10
834:10
716:34
709:10
652:34
645:10
523:.
498:.
473:.
382:)
374:ee
366:.
3303:.
3291::
3274:.
3262::
3234:.
3202:.
3172:.
3142:.
3108:.
3077:.
3029:9
2918:.
2900:.
2879:.
2848:.
2815:.
2780:.
2712:.
2595:n
2592:+
2585:n
2582:+
2566:/
2531:n
2526:n
2523:+
2521:.
2519:+
2513:n
2508:n
2505:+
2401:3
2397:9
2390:4
2386:4
2354:|
2347:)
2344:x
2341:(
2338:f
2334:x
2326:x
2323:d
2318:)
2315:x
2312:(
2309:f
2306:d
2299:|
2274:)
2270:|
2263:)
2260:x
2257:(
2254:f
2250:x
2242:x
2239:d
2234:)
2231:x
2228:(
2225:f
2222:d
2215:|
2211:(
2189:)
2186:x
2180:f
2177:o
2171:s
2168:e
2165:r
2162:u
2159:g
2156:i
2153:f
2147:t
2144:n
2141:a
2138:c
2135:i
2132:f
2129:i
2126:n
2123:g
2120:i
2117:s
2114:(
2104:)
2101:)
2098:x
2095:(
2092:f
2086:f
2083:o
2077:s
2074:e
2071:r
2068:u
2065:g
2062:i
2059:f
2053:t
2050:n
2047:a
2044:c
2041:i
2038:f
2035:i
2032:n
2029:g
2026:i
2023:s
2020:(
2006:x
2002:x
1988:)
1985:x
1982:(
1979:f
1947:)
1944:x
1941:(
1938:f
1916:9
1904:1
1900:1
1876:b
1872:a
1868:a
1812:2
1805:2
1798:2
1791:3
1757:6
1752:0
1744:0
1742:2
1739:2
1707:2
1700:4
1693:2
1656:½
1651:v
1645:m
1636:½
1631:r
1629:π
1624:r
1615:π
1578:x
1576:σ
1572:x
1556:x
1545:x
1516:x
1514:σ
1507:x
1494:x
1492:σ
1473:x
1460:t
1457:s
1454:e
1451:b
1447:x
1435:x
1433:σ
1426:x
1421:x
1419:σ
1412:x
1396:x
1383:t
1380:s
1377:e
1374:b
1370:x
1329:p
1323:1
1320:+
1314:)
1310:|
1306:x
1302:|
1298:(
1279:=
1276:n
1251:)
1244:n
1236:x
1231:(
1216:n
1198:p
1194:x
1183:—
1180:0
1069:—
1066:0
1055:1
951:n
946:n
921:n
914:n
910:n
902:n
894:n
840:×
832:×
788:3
771:0
743:.
730:s
722:J
702:)
699:0
696:(
690:=
687:h
666:s
658:J
635:=
632:h
609:π
600:π
512:(
439:)
433:(
428:)
424:(
410:.
260:e
253:t
246:v
141:)
135:(
130:)
126:(
116:·
109:·
102:·
95:·
64:.
41:.
34:.
20:)
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