# Converting Repeating Decimals to Common Fractions

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Repeating and terminating decimals and converting those to fractions are giving me a lot of trouble. Please help!

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The expert converts the repeating decimals to common fractions.

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I have provided an example problem for each of the ones you submitted. Just plug in your own numbers and you're all set!

(a) 0.432

Example: Convert 0.45 to a fraction.

Step 1: Let x = 0.45.

Step 2: Count how many numbers there are after the decimal point. In this case, there are 2.

Step 3: Multiply both sides by 100, because 100 has 2 zeroes. We get 100x = 45.

Step 4: Solve for x. In this case x = 45/100. Reduce to get x = 9/20.

(b) 0.1 repeating = 0.111111.....

Rule: All single-digit repeating decimal number can be written as a fraction with 9 as the denominator and the repeating single-digit as the numerator.

0.111... = 1/9

0.222... = 2/9

0.333... = 3/9

0.444... = 4/9

0.555... = 5/9

0.666... = 6/9

0.777... = 7/9

0.888... = 8/9

(C) 0.01 REPEATING = 0.0111111....

Example: Convert 0.022222

Since there are 6 digits in 022222, the very last digit is the "1000000th" decimal place.

So we can just say that .022222 is the same as 022222/1000000.

We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 2, since it's the GCD. This gives us 11111/500000.

(D) 0.01 REPEATING = 0.010101010....

Example: Convert 0.131313

Slide the decimal point in this number to the right 2 ...

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