Math CentralQuandaries & Queries


Question from Kenneth:


Why is it recommended to move the decimal from a divisor when dividing so that the divisor is a whole number?
I know how to divide by moving the decimal from the divisor, but I cannot explain the reason.

I thank you for your reply.

Hi Kenneth,

The reason is to help you decide where to put the decimal in the answer.

Suppose you want to divide 0.01247 by 0.0043. You can use long division to divide 1247 by 43 and get 29 but where is the decimal in $0.01247 \div 0.0043?$

One way to answer this question is to use equivalent fractions. In the fraction $\large \frac{0.01247}{0.0043}$ multiply the numerator and denominator by $10000$ to get

\[\frac{0.01247}{0.0043} = \frac{124.7}{43}.\]

Now long division gives $0.01247\div 0.0043 = 124.7\div43 = 2.9.$

I hope this helps,

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