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4.8 Division of a decimal by a whole number

If the divisor is a whole number, the division procedure is almost exactly like the long division procedure
for whole numbers. The only difference is this: a decimal point is placed where the quotient will go,
vertically aligned with the decimal point in the dividend. Forexample, to set up the division 12.0342÷31,
we write, as before

31 12. 0342

Then we put a decimal point vertically aligned with the decimal point in the dividend, where the quotient
will go:

.
31 12. 0342

Now the long division is performed with no further attention paidto the decimal point. In this example,
since 31 is bigger than 12, we put 0 in the units place of the quotient. Continuing, we estimate that 31
goes into 120 3 times, so 3 is placed in the next (tenths) place in the quotient, and 3× 31 is subtracted
from 120 to yield 27. (Note that the decimal point between 2 and 0 is ignored at this point.)

0. 3

31 12. 0342
− 93
27

We bring down the next digit in the dividend, which is 3, and start over with a new dividend of 273.
We estimate that 31 goes into 273 8 times. 8 × 31 = 248, which is subtracted from 273 to yield 25.

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