Esse n t i a l U n d e r st a n d i n g You can use p ercen ts to com pare estim ated or
m easu red values to actual or exact values.Think
What does the
percent error tell you?
The percent error
tells how accurate
a measurement or
estimate is.
Key Concept Relative Error
Relative error is th e ratio of the absolute value of th e difference of a m easu red (or
estim ated) value a n d an actual value com p ared to th e actual value.
| measured or estimated value — actual value |
relative erro r =-----------------------actual valuet—;— ;------------------------W hen relative error is expressed as a percent, it is called percent error.Problem 3 Fi n d i n g Pe r ce n t Er r o r
Multiple Choice A decorator estimates that a rectangular rug is 5 ft by 8 ft. The rug is
actually 4 ft by 8 ft. What is the percent error in the estimated area?
CA) 0.25% GD 20 % CO 25% CD) 80%
| estimated value — actual value |
acti
15 ( 8 ) - 4 ( 8 ) |p ercen t error = ^ (^) actual value— j—---------------- Write the ratio.
4(8) Substitute.
40 — 3 2 1
= —32------ Multiply.
= Simplify.
= 0.25, or 25% Write the result as a percent.
The estim ated area is off by 25%. The correct answ er is C.
- G o t It? 3. You th in k th at the distance b etw een your house an d a friend’s house
is 5.5 mi. The actual distance is 4.75 mi. W hat is th e p ercen t error in
your estim ation?
In P roblem 3, th e actual m easu rem en ts w ere known. Often you d o n ’t know actual
m easurem ents, b u t you know how precise your m easu rem en ts can be.
Think about the last tim e you u sed a ruler. B ecause th e precision of a ru ler is
lim ited, you m easu red to th e n ea rest u n it or fraction of a unit, such as centim eters
or q u arte r inches. The m ost any m easu rem en t can b e off by is o n e half of th e u nit
used in m easuring.
146 Ch ap t er 2 So l v i n g Eq u a t i o n s