Page 336 - Basic College Mathematics with Early Integers

S E C T I O N 4.4 I DIVIDING DECIMALS 313

Concept Check If a quotient is to be rounded to the nearest thousandth, to
what place should the division be carried out? (Assume that the division carries
out to your answer.)

Objective Estimating when Dividing Decimals
Just as for addition, subtraction, and multiplication of decimals, we can estimate
when dividing decimals to check the reasonableness of our answer.

Example 7 Divide: 272.356 , 28.4. Then estimate to see whether the pro- PRACTICE 7
posed result is reasonable. Divide: 713.7 , 91.5. Then
Solution: estimate to see whether the
proposed answer is reasonable.
Exact: Estimate 1 Estimate 2
9.59 9 10
or
284.2723.56 30270 30300
ƒ ƒ
-2556
167 5
-142 0
25 56
-25 56
0

The estimate is 9 or 10, so 9.59 is reasonable.
Work Practice 7

Objective Dividing Decimals by Powers of 10
As with multiplication, there are patterns that occur when we divide decimals by
powers of 10 such as 10, 100, 1000, and so on.
569.2 =56.92
10 Move the decimal point 1 place to the left.
1 zero
569.2
=0.05692
10,000 Move the decimal point 4 places to the left.
4 zeros
This pattern suggests the following rule:

Dividing Decimals by Powers of 10 such as 10, 100, or 1000

Move the decimal point of the dividend to the left the same number of places as
there are zeros in the power of 10.

Examples Divide. PRACTICE 8–9
Divide.
786.1
8. =0.7861 128.3 -0.56
1000 Move the decimal point 3 places to the left. 8. 9.
1000 10
3 zeros
–0.12 Answers
9. =–0.012 Move the decimal point 1 place to the left. 7. Exact: 7.8 8. 0.1283 9. -0.056
10
1 zero
Concept Check Answer
Work Practice 8–9 ten-thousandths place