Convert Repeating Decimals to Fractions

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal fraction that eventually repeats the same sequence of digits indefinitely.

Front

How do you convert a repeating decimal to a fraction?

Back

To convert a repeating decimal to a fraction, set the decimal equal to a variable, multiply by a power of 10 to shift the decimal point, and then subtract the original equation from this new equation.

Front

Convert 0.444... to a fraction.

Back

4/9

Front

Convert 0.333... to a fraction.

Back

1/3

Front

Convert 1.5555... to a fraction.

Back

14/9

Front

Convert -0.467467467... to a fraction.

Back

-467/999

Front

Convert 0.252525... to a fraction.

Back

25/99

Front

What is the significance of the denominator in a fraction derived from a repeating decimal?

Back

The denominator often consists of 9s for each digit in the repeating part, and 10s for any non-repeating part.

Front

What is the first step in converting a repeating decimal to a fraction?

Back

Identify the repeating part and set the decimal equal to a variable.

Front

What does the notation 0.666... represent?

Back

It represents the fraction 2/3.