360 Chapter 4 Decimals
EXAMPLE (^3) Divide:
Strategy We will write the problem in long division form, place a decimal point
directly above the decimal point in 19.2, and divide. If necessary, we will write
additional zeros to the right of the 2 in 19.2.
WHY Writing additional zeros to the right of the 2 allows us to continue the
division process until we obtain a remainder of 0 or the digits in the quotient repeat
in a pattern.
Solution
We can write a zero to the right of 2 in the dividend and continue the division
process. Recall that writing additional zeros to the right of the decimal point does
not change the value of the decimal.That is,.
Check:
Since this is the dividend, the result checks.
3.84
5
19.20
Write a zero to the right of the 2 and bring it down.Continue to divide.The remainder is 0.3.84
5 19.2 0
15
4 2
4 0
20
20
0
19.2 19.20
After subtracting 15 from 19, bring down the 2 and continue to divide.All the digits in the dividend have been used, but the remainder is not 0.3.8
(^5) 19.2
15
4 2
4 0
2
19.2 5
Self Check 3
Divide:
Now Try Problem 2342.8 8
2 Divide a decimal by a decimal.
To develop a rule for division involving a decimal divisor, let’s consider the problem
, where the divisor is the decimal 0.36. First, we express the division in
fraction form.
can be represented by0.2592
0.36
0.360.2592
0.360.2592
Divisor
To be able to use the rule for dividing decimals by a whole number discussed earlier,
we need to move the decimal point in the divisor 0.36 two places to the right.This can
be accomplished by multiplying it by 100. However, if the denominator of the fraction
is multiplied by 100, the numerator must also be multiplied by 100 so that the fraction
maintains the same value.It follows that is the form of 1 that we should use to build^100100
.Multiply by a form of 1.Multiplying both decimals by 100 moves
their decimal points two places to the right.25.92
36
Multiply the numerators.
Multiply the denominators.0.2592 100
0.36 100
0.2592
0.36
0.2592
0.36
100
100
0.2592
0.36^