25:
698:
302:
A set of sequential indices may be used to enumerate elements (or subsets) of a set of ratios under study. For example, in finance, one could define I by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc. The reason for using
546:
299:, all considered in the broad sense. For example, miles per hour in transportation is the output (or benefit) in terms of miles of travel, which one gets from spending an hour (a cost in time) of traveling (at this velocity).
172:) variable. In some cases, it may be regarded as a change to a value, which is caused by a change of a value in respect to another value. For example, acceleration is a change in velocity with respect to time
303:
indices I is so a set of ratios (i=0, N) can be used in an equation to calculate a function of the rates such as an average of a set of ratios. For example, the average velocity found from the set of v
551:
693:{\displaystyle {\begin{aligned}{\mbox{Average rate of change}}&={\frac {f(x+h)-f(x)}{h}}\\{\mbox{Instantaneous rate of change}}&=\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}\end{aligned}}}
738:
of a car can be calculated using the total distance traveled between two points, divided by the travel time. In contrast, the instantaneous velocity can be determined by viewing a
458:
156:(or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an
404:
538:
518:
498:
478:
424:
375:
326:
of a ratio r is 1/r = b/a. A rate may be equivalently expressed as an inverse of its value if the ratio of its units is also inverse. For example, 5
214:. In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate; for example, a
1024:
See
Webster's New International Dictionary of the English Language, 2nd edition, Unabridged. Merriam Webster Co. 2016. p.2065 definition 3.
951:, the amount paid for working a given amount of time (or doing a standard amount of accomplished work) (ratio of payment to time)
89:
288:
Rates and ratios often vary with time, location, particular element (or subset) of a set of objects, etc. Thus they are often
61:
42:
68:
1068:
108:
75:
1034:
46:
57:
921:, the price a borrower pays for the use of the money they do not own (ratio of payment to amount borrowed)
429:
924:
828:
751:
35:
307:'s mentioned above. Finding averages may involve using weighted averages and possibly using the
323:
289:
271:
267:
237:
161:
915:, the ratio of the change in the general price level during a year to the starting price level
82:
933:, the ratio of money gained or lost on an investment relative to the amount of money invested
887:
153:
122:
873:, the number of symbol changes (signaling events) made to the transmission medium per second
314:
A ratio r=a/b has both a numerator "a" and a denominator "b". The value of a and b may be a
1090:
824:
157:
145:
380:
8:
853:, the amount of radioactive material in which one nucleus decays per second, measured in
844:
968:, the number of births or deaths scaled to the size of that population, per unit of time
1100:
945:, the ratio of the number of people who are unemployed to the number in the labor force
523:
503:
483:
463:
409:
360:
296:
169:
1064:
942:
850:
802:
770:
207:
827:, the volume of fluid which passes through a given surface per unit of time; e.g.,
790:
867:, the number of bits that are conveyed or processed by a computer per unit of time
782:
757:
1095:
965:
930:
912:
806:
786:
230:
1084:
1027:
971:
918:
906:
876:
818:
331:
308:
263:
255:
226:
222:
974:, the proportion of the population over age fifteen that can read and write
810:
776:
870:
739:
315:
211:
129:
990:
961:
893:
728:
259:
215:
183:
927:, market price per share of stock divided by annual earnings per share
779:, the rate of change in speed, or the change in speed per unit of time
977:
854:
840:
796:
335:
199:
345:
The speed of the car (often expressed in miles per hour) is a rate.
295:
A rate (or ratio) may often be thought of as an output-input ratio,
236:
A rate defined using two numbers of the same units will result in a
24:
995:
936:
864:
251:
149:
141:
137:
799:, the number of occurrences of a repeating event per unit of time
341:
Rates are relevant to many aspects of everyday life. For example:
319:
164:(the fraction numerator) of the rate expresses the corresponding
890:, number of reinforcements per unit of time, usually per minute
195:
980:
or gender ratio, the ratio of males to females in a population
1005:
1000:
766:
735:
283:
242:
203:
179:
1063:(3rd ed.). Addison-Wesley Publishers Ltd. p. 129.
948:
327:
187:
221:
Rates that have a non-time divisor or denominator include
879:, the number of samples (signal measurements) per second
178:
is a common type of rate ("per unit of time"), such as
16:
Ratio between two related quantities in different units
1035:"IEC 60050 - Details for IEV number 112-03-18: "rate""
909:, how much one currency is worth in terms of the other
615:
555:
727:. An instantaneous rate of change is equivalent to a
549:
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486:
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432:
412:
383:
363:
49:. Unsourced material may be challenged and removed.
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900:
1082:
629:
349:The amount of interest paid per year is a rate.
347:What interest does your savings account pay you?
939:, the tax amount divided by the taxable income
821:, the speed at which chemical reactions occur
258:). Dimensionless rates can be expressed as a
773:, or the change of position per unit of time
426:happens to be the denominator of the rate
277:
1039:International Electrotechnical Vocabulary
109:Learn how and when to remove this message
834:
334:(kWh) corresponds to 1/5 kWh/mi (or 200
540:) can be formally defined in two ways:
1083:
896:, usually measured in beats per minute
357:Consider the case where the numerator
1058:
218:is expressed as "beats per minute".
47:adding citations to reliable sources
18:
13:
711:) is the function with respect to
14:
1112:
745:
453:{\displaystyle \delta f/\delta a}
352:
23:
34:needs additional citations for
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1018:
955:
901:Economics/finance rates/ratios
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1:
1011:
617:Instantaneous rate of change
202:, a count per second (i.e.,
7:
1061:Calculus: A Complete Course
984:
883:Miscellaneous definitions:
10:
1117:
838:
762:In chemistry and physics:
755:
749:
281:
120:
1059:Adams, Robert A. (1995).
793:transferred per unit time
734:For example, the average
343:How fast are you driving?
262:(for example, the global
148:, often represented as a
769:, the rate of change of
377:of a rate is a function
829:cubic meters per second
715:over the interval from
278:Properties and examples
58:"Rate" mathematics
694:
557:Average rate of change
534:
514:
494:
474:
460:. A rate of change of
454:
420:
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371:
290:mathematical functions
238:dimensionless quantity
233:(in volts per meter).
888:Rate of reinforcement
835:Counts-per-time rates
695:
535:
515:
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475:
455:
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372:
282:Further information:
254:) or counts (such as
925:Price–earnings ratio
825:Volumetric flow rate
785:, the rate of doing
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524:
504:
484:
464:
430:
410:
399:{\displaystyle f(a)}
381:
361:
158:independent variable
146:units of measurement
121:For other uses, see
43:improve this article
845:Aperiodic frequency
789:, or the amount of
690:
688:
643:
619:
559:
530:
520:is incremented by
510:
490:
470:
450:
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367:
297:benefit-cost ratio
266:in 1998 was 80%),
190:. In fact, often
943:Unemployment rate
851:Radioactive decay
803:Angular frequency
684:
628:
618:
608:
558:
533:{\displaystyle h}
513:{\displaystyle a}
493:{\displaystyle a}
473:{\displaystyle f}
419:{\displaystyle a}
370:{\displaystyle f}
208:radio frequencies
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813:per unit of time
809:, the number of
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480:with respect to
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240:, also known as
194:is a synonym of
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100:
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51:
27:
19:
1116:
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839:Main articles:
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758:Time derivative
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750:Main category:
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246:or simply as a
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11:
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993:
986:
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975:
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966:mortality rate
957:
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931:Rate of return
928:
922:
916:
913:Inflation rate
910:
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860:In computing:
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815:
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807:rotation speed
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752:Temporal rates
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746:Temporal rates
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353:Rate of change
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231:electric field
227:literacy rates
223:exchange rates
168:in the other (
166:rate of change
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29:
22:
15:
9:
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1070:0-201-82823-5
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1041:(in Japanese)
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1021:
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1002:
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988:
979:
976:
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972:Literacy rate
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950:
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941:
938:
935:
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929:
926:
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919:Interest rate
917:
914:
911:
908:
907:Exchange rate
905:
904:
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877:Sampling rate
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819:Reaction rate
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390:
384:
364:
350:
348:
344:
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333:
332:kilowatt-hour
329:
325:
321:
317:
312:
310:
309:harmonic mean
300:
298:
293:
291:
285:
275:
273:
269:
265:
264:literacy rate
261:
257:
256:literacy rate
253:
249:
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228:
224:
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213:
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201:
197:
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177:
176:Temporal rate
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147:
144:in different
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102:
99:February 2015
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63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
1060:
1054:
1043:. Retrieved
1038:
1029:
1020:
882:
859:
777:Acceleration
761:
733:
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702:
356:
346:
342:
340:
313:
301:
294:
287:
247:
241:
235:
220:
212:sample rates
191:
175:
174:
165:
160:), then the
133:
127:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
1091:Measurement
956:Other rates
871:Symbol rate
740:speedometer
316:real number
130:mathematics
1085:Categories
1045:2023-09-13
1012:References
991:Derivative
962:Birth rate
894:Heart rate
855:becquerels
756:See also:
729:derivative
260:percentage
216:heart rate
184:heart rate
142:quantities
69:newspapers
1101:Quotients
978:Sex ratio
949:Wage rate
841:Frequency
797:Frequency
666:−
637:→
590:−
445:δ
434:δ
330:(mi) per
252:tax rates
250:(such as
206:); e.g.,
200:frequency
170:dependent
152:. If the
996:Gradient
985:See also
937:Tax rate
865:Bit rate
771:position
272:multiple
268:fraction
162:dividend
150:fraction
138:quotient
500:(where
324:inverse
320:integer
154:divisor
140:of two
136:is the
83:scholar
1067:
964:, and
791:energy
703:where
406:where
338:/mi).
322:. The
229:, and
196:rhythm
186:, and
85:
78:
71:
64:
56:
1096:Rates
1006:Slope
1001:Hertz
811:turns
783:Power
767:Speed
736:speed
328:miles
284:Ratio
270:, or
243:ratio
204:hertz
180:speed
90:JSTOR
76:books
1065:ISBN
843:and
805:and
787:work
248:rate
192:rate
188:flux
134:rate
132:, a
123:Rate
62:news
719:to
630:lim
318:or
210:or
198:or
128:In
45:by
1087::
1037:.
742:.
731:.
336:Wh
311:.
305:I
292:.
274:.
225:,
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717:a
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709:x
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669:f
663:)
660:h
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654:x
651:(
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626:=
606:h
602:)
599:x
596:(
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584:h
581:+
578:x
575:(
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566:=
528:h
508:a
488:a
468:f
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441:/
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394:)
391:a
388:(
385:f
365:f
125:.
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
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