36:
709:
313:
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
557:
310:, 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).
183:) 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
314:
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
562:
704:{\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}}}
749:
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
469:
167:(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
415:
549:
529:
509:
489:
435:
386:
337:
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
225:. 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
1035:
See
Webster's New International Dictionary of the English Language, 2nd edition, Unabridged. Merriam Webster Co. 2016. p.2065 definition 3.
53:
1079:
119:
962:, the amount paid for working a given amount of time (or doing a standard amount of accomplished work) (ratio of payment to time)
100:
299:
Rates and ratios often vary with time, location, particular element (or subset) of a set of objects, etc. Thus they are often
72:
57:
79:
86:
46:
1045:
935:
68:
839:
762:
932:, the price a borrower pays for the use of the money they do not own (ratio of payment to amount borrowed)
334:
300:
282:
278:
248:
172:
898:
164:
133:
440:
1101:
835:
168:
156:
855:
1111:
307:
180:
318:'s mentioned above. Finding averages may involve using weighted averages and possibly using the
1075:
953:
926:, the ratio of the change in the general price level during a year to the starting price level
861:
813:
781:
218:
93:
944:, the ratio of money gained or lost on an investment relative to the amount of money invested
884:, the number of symbol changes (signaling events) made to the transmission medium per second
801:
325:
A ratio r=a/b has both a numerator "a" and a denominator "b". The value of a and b may be a
17:
793:
768:
391:
864:, the amount of radioactive material in which one nucleus decays per second, measured in
979:, the number of births or deaths scaled to the size of that population, per unit of time
1106:
976:
956:, the ratio of the number of people who are unemployed to the number in the labor force
941:
923:
817:
797:
534:
514:
494:
474:
420:
371:
241:
1095:
982:
929:
917:
887:
829:
342:
319:
274:
266:
237:
233:
838:, the volume of fluid which passes through a given surface per unit of time; e.g.,
821:
787:
878:, the number of bits that are conveyed or processed by a computer per unit of time
881:
750:
326:
222:
140:
35:
1001:
972:
904:
739:
270:
226:
194:
988:
865:
851:
807:
346:
210:
985:, the proportion of the population over age fifteen that can read and write
1006:
947:
875:
262:
160:
152:
148:
330:
938:, market price per share of stock divided by annual earnings per share
790:, the rate of change in speed, or the change in speed per unit of time
206:
356:
The speed of the car (often expressed in miles per hour) is a rate.
306:
A rate (or ratio) may often be thought of as an output-input ratio,
247:
A rate defined using two numbers of the same units will result in a
1016:
1011:
810:, the number of occurrences of a repeating event per unit of time
777:
746:
352:
Rates are relevant to many aspects of everyday life. For example:
294:
253:
214:
190:
175:(the fraction numerator) of the rate expresses the corresponding
959:
338:
198:
901:, number of reinforcements per unit of time, usually per minute
991:
or gender ratio, the ratio of males to females in a population
29:
1074:(3rd ed.). Addison-Wesley Publishers Ltd. p. 129.
232:
Rates that have a non-time divisor or denominator include
890:, the number of samples (signal measurements) per second
189:
is a common type of rate ("per unit of time"), such as
27:
Ratio between two related quantities in different units
1046:"IEC 60050 - Details for IEV number 112-03-18: "rate""
920:, how much one currency is worth in terms of the other
626:
566:
738:. An instantaneous rate of change is equivalent to a
560:
537:
517:
497:
477:
443:
423:
394:
374:
60:. Unsourced material may be challenged and removed.
703:
543:
523:
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483:
463:
429:
409:
380:
640:
360:The amount of interest paid per year is a rate.
358:What interest does your savings account pay you?
950:, the tax amount divided by the taxable income
832:, the speed at which chemical reactions occur
269:). Dimensionless rates can be expressed as a
8:
784:, or the change of position per unit of time
437:happens to be the denominator of the rate
1050:International Electrotechnical Vocabulary
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559:
536:
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393:
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120:Learn how and when to remove this message
345:(kWh) corresponds to 1/5 kWh/mi (or 200
1028:
551:) can be formally defined in two ways:
907:, usually measured in beats per minute
368:Consider the case where the numerator
229:is expressed as "beats per minute".
7:
58:adding citations to reliable sources
722:) is the function with respect to
25:
464:{\displaystyle \delta f/\delta a}
34:
45:needs additional citations for
912:Economics/finance rates/ratios
688:
682:
673:
661:
647:
612:
606:
597:
585:
404:
398:
1:
628:Instantaneous rate of change
213:, a count per second (i.e.,
18:Rate of change (mathematics)
1072:Calculus: A Complete Course
894:Miscellaneous definitions:
1128:
849:
773:In chemistry and physics:
766:
760:
292:
131:
1070:Adams, Robert A. (1995).
804:transferred per unit time
745:For example, the average
354:How fast are you driving?
273:(for example, the global
159:, often represented as a
780:, the rate of change of
388:of a rate is a function
840:cubic meters per second
726:over the interval from
289:Properties and examples
69:"Rate" mathematics
705:
568:Average rate of change
545:
525:
505:
485:
471:. A rate of change of
465:
431:
411:
382:
301:mathematical functions
249:dimensionless quantity
244:(in volts per meter).
899:Rate of reinforcement
846:Counts-per-time rates
706:
546:
526:
506:
486:
466:
432:
412:
383:
293:Further information:
265:) or counts (such as
936:Price–earnings ratio
836:Volumetric flow rate
796:, the rate of doing
558:
535:
515:
495:
475:
441:
421:
410:{\displaystyle f(a)}
392:
372:
169:independent variable
157:units of measurement
132:For other uses, see
54:improve this article
856:Aperiodic frequency
800:, or the amount of
701:
699:
654:
630:
570:
541:
531:is incremented by
521:
501:
481:
461:
427:
407:
378:
308:benefit-cost ratio
277:in 1998 was 80%),
201:. In fact, often
954:Unemployment rate
862:Radioactive decay
814:Angular frequency
695:
639:
629:
619:
569:
544:{\displaystyle h}
524:{\displaystyle a}
504:{\displaystyle a}
484:{\displaystyle f}
430:{\displaystyle a}
381:{\displaystyle f}
219:radio frequencies
130:
129:
122:
104:
16:(Redirected from
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1086:
1085:
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1058:
1057:
1042:
1036:
1033:
824:per unit of time
820:, the number of
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510:
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491:with respect to
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251:, also known as
205:is a synonym of
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
1127:
1126:
1122:
1121:
1120:
1118:
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1116:
1092:
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1089:
1082:
1069:
1068:
1064:
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1025:
998:
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914:
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850:Main articles:
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769:Time derivative
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761:Main category:
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698:
697:
657:
632:
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621:
581:
572:
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472:
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419:
418:
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370:
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317:
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257:or simply as a
137:
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115:
109:
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63:
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39:
28:
23:
22:
15:
12:
11:
5:
1125:
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1080:
1062:
1037:
1027:
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1021:
1020:
1019:
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986:
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977:mortality rate
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965:
964:
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951:
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942:Rate of return
939:
933:
927:
924:Inflation rate
921:
913:
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902:
892:
891:
885:
879:
871:In computing:
869:
868:
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844:
843:
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833:
827:
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818:rotation speed
805:
791:
785:
763:Temporal rates
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757:Temporal rates
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712:
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364:Rate of change
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242:electric field
238:literacy rates
234:exchange rates
179:in the other (
177:rate of change
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42:
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33:
26:
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14:
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10:
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1081:0-201-82823-5
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1052:(in Japanese)
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1038:
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1018:
1015:
1013:
1010:
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1005:
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987:
984:
983:Literacy rate
981:
978:
974:
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966:
961:
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946:
943:
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930:Interest rate
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922:
919:
918:Exchange rate
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888:Sampling rate
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830:Reaction rate
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733:
729:
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721:
717:
692:
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609:
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582:
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574:
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552:
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518:
498:
478:
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401:
395:
375:
363:
361:
359:
355:
350:
348:
344:
343:kilowatt-hour
340:
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332:
328:
323:
321:
320:harmonic mean
311:
309:
304:
302:
296:
288:
286:
284:
280:
276:
275:literacy rate
272:
268:
267:literacy rate
264:
260:
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187:Temporal rate
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158:
155:in different
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135:
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113:
110:February 2015
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81:
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74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
1071:
1065:
1054:. Retrieved
1049:
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1031:
893:
870:
788:Acceleration
772:
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731:
727:
723:
719:
715:
713:
367:
357:
353:
351:
324:
312:
305:
298:
258:
252:
246:
231:
223:sample rates
202:
186:
185:
176:
171:), then the
144:
138:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
1102:Measurement
967:Other rates
882:Symbol rate
751:speedometer
327:real number
141:mathematics
1096:Categories
1056:2023-09-13
1023:References
1002:Derivative
973:Birth rate
905:Heart rate
866:becquerels
767:See also:
740:derivative
271:percentage
227:heart rate
195:heart rate
153:quantities
80:newspapers
1112:Quotients
989:Sex ratio
960:Wage rate
852:Frequency
808:Frequency
677:−
648:→
601:−
456:δ
445:δ
341:(mi) per
263:tax rates
261:(such as
217:); e.g.,
211:frequency
181:dependent
163:. If the
1007:Gradient
996:See also
948:Tax rate
876:Bit rate
782:position
283:multiple
279:fraction
173:dividend
161:fraction
149:quotient
511:(where
335:inverse
331:integer
165:divisor
151:of two
147:is the
94:scholar
1078:
975:, and
802:energy
714:where
417:where
349:/mi).
333:. The
240:, and
207:rhythm
197:, and
96:
89:
82:
75:
67:
1107:Rates
1017:Slope
1012:Hertz
822:turns
794:Power
778:Speed
747:speed
339:miles
295:Ratio
281:, or
254:ratio
215:hertz
191:speed
101:JSTOR
87:books
1076:ISBN
854:and
816:and
798:work
259:rate
203:rate
199:flux
145:rate
143:, a
134:Rate
73:news
730:to
641:lim
329:or
221:or
209:or
139:In
56:by
1098::
1048:.
753:.
742:.
347:Wh
322:.
316:I
303:.
285:.
236:,
193:,
1084:.
1059:.
736:h
734:+
732:a
728:a
724:x
720:x
718:(
716:f
693:h
689:)
686:x
683:(
680:f
674:)
671:h
668:+
665:x
662:(
659:f
651:0
645:h
637:=
617:h
613:)
610:x
607:(
604:f
598:)
595:h
592:+
589:x
586:(
583:f
577:=
539:h
519:a
499:a
479:f
459:a
452:/
448:f
425:a
405:)
402:a
399:(
396:f
376:f
136:.
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
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