Math: decimals to fractions

Tutoring middle school math, you get asked how to convert decimals to fractions.  The math tutor tells some obvious – and some less obvious – methods.

Converting a terminating decimal (one that ends) to a fraction is easy:

Step 1)  Notice how many digits are right of the decimal point.

Step 2)  Write the decimal digits on the top of the fraction. Then, on the bottom, write a 1 followed by the same number of zeros as there are digits to the right of the decimal point.

Step 3)  Reduce if necessary.

Example:  Convert 0.0015 to a fraction.

Step 1) There are four digits to the right of the decimal point.

Step 2) Initially, our fraction is 15/10000. Notice that we need four zeros on the bottom, since there were four digits to the right of the decimal point.

Step 3) We reduce 15/10000 to 3/2000. We get this answer from realizing that 5 divides into both the numerator and the denominator: 3 times into the numerator, and 2000 times into the denominator.

To convert a repeating decimal, there are a couple of shortcuts. Specifically, if a single digit is repeating, the equivalent fraction is that digit over 9. If a pattern of two digits repeats, the equivalent fraction is those two digits over 99.

Example: Convert 0.5555….. to a fraction.

Solution: The fraction is 5/9.

Example: Convert 0.17171717……to a fraction.

Solution: The fraction is 17/99.

For middle school purposes, the above techniques are probably enough. There is related content in my earlier blog article here. For those interested in reading further, please visit again:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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