Converting Repeating Decimals to Fractions

What is the shortcut for converting repeating decimals to fractions?

• For every repeating digit, there will be a 9 in the numerator.

• For every repeating digit, there will be a 9 in the denominator.

• For every non-repeating digit, there will be a 9 in the denominator.

• For every non-repeating digit, there will be a 9 in the numerator.

In the first example, what is the fraction form of 0.45 repeating?

• 5/11

• 45/99

• 9/45

• 11/5

How do you simplify the fraction 45/99?

• Divide both numerator and denominator by 9

• Divide both numerator and denominator by 3

• Divide both numerator and denominator by 5

• Divide both numerator and denominator by 11

In the second example, what is the denominator for 0.83 with 3 repeating?

• 9

• 90

• 100

• 99

What is the numerator for the fraction form of 0.83 with 3 repeating?

• 75

• 83

• 8

• 3

In the third example, what is the fraction form of 0.012 with 2 repeating?

• 12/100

• 11/900

• 1/12

• 2/100

How do you determine the numerator for 0.012 with 2 repeating?

• Subtract the repeating part from the whole decimal

• Subtract the non-repeating part from the whole decimal

• Add the repeating part to the whole decimal

• Add the non-repeating part to the whole decimal

In the fourth example, what is the fraction form of 0.156 with 56 repeating?

• 31/198

• 156/990

• 56/100

• 15/90

What is the denominator for the fraction form of 0.156 with 56 repeating?

• 99

• 198

• 900

• 990

How do you simplify the fraction 155/990?

• Divide both numerator and denominator by 3

• Divide both numerator and denominator by 11

• Divide both numerator and denominator by 5

• Divide both numerator and denominator by 9