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### Relative Errors

```
Date: 08/03/97 at 14:09:18
From: Max Wasserman
Subject: Relative errors

How do you find the relative error of a measurement?
```

```
Date: 08/04/97 at 08:53:32
From: Doctor Jerry
Subject: Re: Relative errors

Hi Max,

Suppose you are measuring someone's height.  If her actual, true
height is 60 inches and you measure 61 inches, then the absolute
error of measurement is 61-60 = 1 inch.  The percentage error is
[(61-60)/60]*100 = [1/60]*100 = 5/3, which is a little less than
a 1 percent error.

The relative error is just (61-60)/60 = 1/60.  The idea is that
if you make an error of 1 inch in measuring a person's height,
this is a relatively large error compared to making an error of
1 inch in measuring the length of a one-mile racetrack. The
absolute errors would be the same, but the relative errors would be
1/60 and [(5280*12+1)-5280*12]/(5280*12)=1/(5280*12), which is
quite a bit smaller than 1/60.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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