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I4trhen we measure, we are sometimes limited by the accuracy of the tools we haveor by the accuracy of the person who is actually measuring. The enor is the ab-

solute value of the difference between the two values. The percent of error is theratio of the eror to the true value, written as a percent:

Error = lactual measure - observed measurel

Percent of error =CITOT lrcfual measu-re - observed meas

I

x 100"r

x 100achlal measu.re

MODEL PROBTEMS

ft42 Ghapter O: Ratio ,ond Proportion

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1 Our bathroom scales are often inaccurate. We go to the doctor for a checkup and find a discrepanry.If you get a reading of 113 pounds on your bathroom scale and a reading of 111 pounds on the doc-tor's scale, what is the percerrt of error?

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Percent of eror : x 100

Itrt -- ttel : .2- - 0.01801801802 - -t .Blvo111 111

2 Using the bathroom scale above, Chris weighed L50 pounds. What was his actual weight to the near-est pound?

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From tlre model problem abovg we know that thF percent error is approximgtely 1..80%.

, percent of error - lactual measrile : observed measurel

act'al measnre x 1oo

t rrat

1.80 : lar - 1501 x 100 Multipty both.sides by zrw

/P- +E x 1oo : 't.Bow'7b

We know w - 150is negative. Therefore 150 - ar is positive and lar - 1501 :150 - w.

100(150) 100(zp) : 7.8Aw

15,000 lAAw - !.80w

*]$Aat - *100ru

15,000 _ tffiAyt101.90 ryr.fa

7I) - 747.34n07 Rounded to the nearest pound, w - 147 pounds.

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gravity w3s found to be 9.5 meters per secondsquSred, The accepted acceleration of graviryto this degree of accuracy is g.g metlrs persecond squared.

I4rhat * the approximatepercent of error?

(1) 96.9Vo

(2) 3..'!,6Vo

(3) 3.06Vo

(4) 7.A3Vo

Exercises 2 and 3: A car odometer measured the:g's speed at 55 ryph when the actual speed was**Ph.L Tio the nearest tenth of a percent, what is the

,"*{ercent of errgr for this odorneter?.!'-'-- i

r 3 If the actual speed was 45 mph, what rvouldt'"--trne odom€ter read?

45 kilosrams when the actual weight is S0 kilo-grams

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{" n p the nearest hundredth of a percent, what\v*# rs the percent of error for this siale?

grams, what is the Jctual weight to the

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{.'6 A tt"dent rneasured the volume of a 2-liter

t-****r'Container to be 2.? liters. What was the per-cent of error of the student's measurement tothe nearest hundredth?

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7 A scientist found the density of a metal to be2-35 sam$ /cm'. The accepied varue for thedensi? ir Z.S9 grams/cm3. IrVhat is the per_

' nearest tenth?'

'

l',f'"'i\r, 8 Ght"u stud.ents measured the densi* of a so-?-8"-!-**Fution in a science lab. Their average value

was l.T?s_ g/mL. The accepted varue is1'_.09T g,/ n*. I4lhat is the percent of enor inthe sfudent's measure to the nearest tenth?

9 A census of the popuration undercounted aparticular qo:p py zvo. The numb", oi;;"-ple recorded foi this group was 2,g67. Tc thenearest whole numbet how many members

of this group should have been retorded?L0 An odometer measures the distance a vehicle

travels-, The odometer on Eric's car read65,48a miles before he left Long Island. wi;;he arrived at his cousin's hou-se in oru"g*Counfy, his odometer read 65,s;65 miles. Ttetrtp diltance was actualtl 9O;iils. on a oipfrom New york city to Arbany his odom*i*,display changed from 66/4so rnites to 66,62amiles. Assu*Tg that. the odometer is alwaysh"o.r.ect by _the same percentage, how far

did he actualty travel?LL Hany was stopped on the New York State

Thruway for dfving at an excessive speed.The officer's radar,recorder indicated a speedof 80 Tph. Har{r claimed that altho"gh hewas .drjving too fast, his speedoireterrecorded a speed of T0 miles pei hour. If theradar has a margin of erro. of -F3 mph, whatis the minimur percent of error

"fHurry=

speedometer?

Exercises 72-15:The t**perature of Maddy,soven is always off by the iame percent of error.

She must set the oven temperature to 400o whenshe uses a

1ecip9that calls for roasting at BTS'.

Finish the chart for Maddy so that she can easilyconvert from recrqe temperature to display"eoven temperature. Round all temperatures to-thenearest 5 degrees.

Desiredtemperaturb , Madd/s oven . '',.,, ,

,

12 325

L3 350,\FIF

5/J

14 4AA

1s 425

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Pe,rcent of Error $49