Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 6: Decimals 77

So if that’s how you divide a decimal by a whole number, how do you divide by a decimal?
You don’t. What you do is actually to find an equivalent problem, a problem with the same
answer, in which the divisor is a whole number.

That may sound like magic, but if you stop to think about it, you’ve seen equivalent problems.
You k now t hat 12 z 4 = 3 and 120 z 40 = 3. Those two different problems have the same answer
because both the dividend and the divisor were multiplied by the same number, in that case,
by 10. That will be the secret to decimal division.

MATH TRAP

When you divide decimals, the divisor needs to be a whole number. The dividend

doesn’t. Move the decimal point as many places as it takes to turn the divisor into a

whole number. Move the decimal point in the dividend the same number of places,

whether it becomes a whole number, or still has decimal digits, or needs trailing zeros

added so that you can move enough. The divisor calls the play. Whatever happens to

the divisor happens to the dividend.

When you multiply a decimal by 10, the decimal point moves 1 place to the right. The task of
dividing 81.312 by 3.52 can also be thought of as 813.12 divided by 35.2, or 8131.2 divided by 352.

When you’re faced with a division problem where the divisor is a decimal, move the decimal
point in the divisor to the right until the divisor is a whole number. Move the decimal point in
the dividend the same number of places to the right. Divide normally, just as you would for whole
numbers, and bring the decimal point straight up into the quotient. Here’s an example.

Divide 17.835 by 2.05.

Estimate first. A number almost 18 divided by about 2 should give you an answer close to 9.

Move the decimal point in the divisor, 2.05, two places right so that 2.05 becomes 205. Move the
decimal point in 17.835 two places right as well, making it 1783.5. Then divide.

The decimal point in the dividend, between the 3 and the 5, f loats straight up into the quotient
for a result of 8.7.

205 1783.5)

8.7

1640

1435

1435

0