Repeating Decimals to Fractions

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal fraction that eventually repeats a sequence of digits indefinitely. For example, 0.333... is a repeating decimal because the digit '3' repeats.

Front

Which of the following is a repeating decimal? 2.451836248702165064513549452, 7.1245454545454545454545454545, 8.125, 12.55

Back

7.1245454545454545454545454545 is a repeating decimal.

Front

What is 2/9 as a decimal?

Back

2/9 as a decimal is 0.22222222222222222222222222222222222.

Front

Identify the fraction equivalent to the decimal 2.4444...

Back

The fraction equivalent to 2.4444... is 2 4/9.

Front

What is 23/99 as a decimal?

Back

23/99 as a decimal is 0.2323232323.....

Front

How do you convert a repeating decimal to a fraction?

Back

To convert a repeating decimal to a fraction, let x equal the decimal, multiply by a power of 10 to shift the decimal point, subtract the original equation from this new equation, and solve for x.

Front

What is the decimal representation of 1/3?

Back

1/3 as a decimal is 0.333... (repeating).

Front

What is the decimal representation of 1/6?

Back

1/6 as a decimal is 0.1666... (repeating).

Front

What is the decimal representation of 5/9?

Back

5/9 as a decimal is 0.555... (repeating).

Front

What is the difference between terminating and repeating decimals?

Back

Terminating decimals have a finite number of digits after the decimal point (e.g., 0.5), while repeating decimals have an infinite sequence of digits that repeat (e.g., 0.666...).