Algebra 1 Common Core Student Edition, Grade 8-9

Think
Can a m easurem ent
be o ff by more than
one half of the unit
t h a t is used?
No, n o t i f you m easure
correctly. Suppose you
m easure a le n g th as 8 in.
If you w e re o ff by 0.5 in.
or more, you would have
rounded to e ith e r 7 in.
o r 9 in.

Which difference
should you use?
The g re a te r difference
will result in the greatest
possible percent error, so
use the difference th a t
has th e greatest absolute
value.

Problem 4 Finding M inim um and M axim um Dimensions

Po st er s You are framing a poster and measure the length of the poster as 18.5 in.,

to the nearest half inch. What are the minimum and maximum possible lengths of

the poster?

You m easu red to th e n ea rest 0.5 in., so th e greatest possible error is 0.25 in.

M inim um length = m ea su re d value - possible erro r = 18.5 — 0.25 = 18.25

M axim um length = m e a su re d value + possible erro r = 18.5 + 0.25 = 18.75

The m inim um possible length is 18.25 in. The m axim um is 18.75 in.

v j G o t It? 4. A stu d e n t’s height is m easu red as 66 in. to th e n ea rest inch. W hat are the

stu d e n t’s m in im u m an d m axim um possible heights?

Problem 5 Finding the G reatest Possible Percent Error

Cr af t s The diagram at the right shows the

dimensions of a gift box to the nearest inch.

What is the greatest possible percent error in

calculating the volume of the gift box?

5 in.

&D-QW-

1 The dimensions of the gift box

to the nearest inch

1 The formula for volume:

V - ( w h

1 The g re a te s t possible e rro r in

each d im e n sio n is 0.5 in.

The greatest possible

p e rce n t e rro r in

calculating the volume

6 in.

Plan. ||||h|...........,

Find th e m in im u m and m a xim u m

volum es. Find th e diffe re n ce s b e tw een

the possible volumes and the

measured volume. Use the greater

d iffe re n ce to fin d th e p e rce n t error.

M easured volum e

V = (wh

= (12)(6)(5)

= 360

Minimum volume

V = €wh

= (11.5)(5.5)(4.5)

= 284.625

Maximum volume

V = (wh

= (12.5)(6.5)(5.5)

= 446.875

F ind the differences.

|m in im u m volum e — m ea su re d volum e] = 1284.625 — 3601 = 75.375

| m axim um volum e — m ea su re d volum e | = 1446.875 — 3601 = 86.875

Use th e greater difference to find th e greatest possible p ercen t error.

greater difference in volume

greatest possible p e rc e n t e r r o r : measured volume

86.875

360 Substitute.

= 0.24 or 24% Write th e re s u lt as a percent.

The greatest possible p ercen t error in th e volum e, b ase d on m easu rem en ts to the

n ea rest inch, is ab o u t 24%.

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