Content Area Math 5: Calculators and Repeating Decimals

Calculators are great tools. They help you do math quickly. They show exact answers to difficult problems. Are calculators always right? It depends on what you mean by right. You may be adding, subtracting, or multiplying. Then a calculator will show the exact answer. But dividing is different. Try dividing 10 by 6 on a calculator. You may get 1.6666666. Or you may get 1.6666667. Which is the exact answer, 1.6666666 or 1.6666667? Neither! Both are approximations. They are both right. But neither is exact.

Why do calculators do this? Most of them can’t show fractions. The exact answer to 10 divided by 6 is the mixed number 1 2/3. The calculator has no way to display two-thirds.

Here is a way to understand what is happening. Divide 10 by 6 using paper and pencil. Your problem will look like the one at the left. The answer has a repeating decimal. You can keep dividing forever. You’ll never get an exact answer. The digit 6 in the answer repeats forever.

A calculator that gives 1.6666666 is truncating (cutting off) the answer. It shows as many digits as it can. Then it drops the rest. A calculator that gives 1.6666667 is rounding. Since the last digit is 5 or greater, it shows the next higher digit (7).

For most division problems, it won’t matter if the answer is approximate. But you might have a problem in which you really need the exact answer. Then you may need to use fractions.

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