Basic Mathematics for College Students

Note that the quotients, 0.813 and 81.3, and the dividend, 8.13, are the same except

for the location of the decimal points. The first quotient, 0.813, can be easily obtained

by moving the decimal point of the dividend one place to the left. The second quotient,

81.3, is easily obtained by moving the decimal point of the dividend one place to the

right. These observations illustrate the following rules for dividing a decimal by a

power of 10.

364 Chapter 4 Decimals

Dividing a Decimal by 10, 100, 1,000, and So On

To find the quotient of a decimal and 10, 100, 1,000, and so on, move the

decimal point to the left the same number of places as there are zeros in the

power of 10.

Dividing a Decimal by 0.1, 0.01, 0.001, and So On

To find the quotient of a decimal and 0.1, 0.01, 0.001, and so on, move the

decimal point to the right the same number of decimal places as there are in

the power of 10.

EXAMPLE (^7) Find each quotient:
a. b. c.
StrategyWe will identify the divisor in each division. If it is a power of 10 greater
than 1, we will count the number of zeros that it has. If it is a power of 10 less than
1, we will count the number of decimal places that it has.
WHYThen we will know how many places to the right or left to move the decimal
point in the dividend to find the quotient.
Solution
a. Since the divisor 10 has one zero, move the decimal point one
place to the left.
b. Since the divisor 10,000 has four zeros, move the decimal
point four places to the left. Write three placeholder zeros
(shown in blue).
c. Since the divisor 0.01 has twodecimal places, move the decimal
point in 290.623 twoplaces to the right.

290.623

0.01

29062.3

0.00086

8.610,000. 00086

16.74 10 1.674

290.623

0.01

16.74 10 8.610,000

Self Check 7

Find each quotient:

a.

b.

c.

Now TryProblems 43 and 49

19.44070.0001

1.07

1,000

721.3 100





6 Divide signed decimals.

The rules for dividing integers also hold for dividing signed decimals. The quotient of

two decimals with like signsis positive, and the quotient of two decimals with unlike

signsis negative.

EXAMPLE 8

Divide: a. b.

StrategyIn part a, we will use the rule for dividing signed decimals that have

different (unlike) signs. In part b, we will use the rule for dividing signed decimals

that have the same (like) signs.

38.677

0.1

104.48316.3

Self Check 8

Divide:

a.

b.

23.9

0.1

100.62415.2