Repeating Decimals as Fractions

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal fraction that eventually repeats a digit or a group of digits indefinitely.

Front

How can a repeating decimal be expressed as a fraction?

Back

A repeating decimal can be expressed as a fraction by using algebraic methods, such as setting the decimal equal to a variable and manipulating the equation.

Front

What is the fraction equivalent of the repeating decimal 0.333... ?

Back

The fraction equivalent of 0.333... is 1/3.

Front

What is the process to convert a repeating decimal to a fraction?

Back

1. Let x equal the repeating decimal. 2. Multiply x by a power of 10 to shift the decimal point. 3. Subtract the original equation from this new equation to eliminate the repeating part. 4. Solve for x.

Front

What is the repeating decimal for the fraction 1/6?

Back

The repeating decimal for 1/6 is 0.1666... (or 0.1̅6).

Front

What is the relationship between fractions and their decimal representations?

Back

Every fraction can be represented as a decimal, and some fractions have terminating decimals while others have repeating decimals.

Front

How do you identify the repeating part of a decimal?

Back

The repeating part of a decimal can be identified by looking for a sequence of digits that appears after a certain point and continues indefinitely.

Front

What is the repeating decimal equivalent of 13/37?

Back

The repeating decimal equivalent of 13/37 is approximately 0.351351... (or 0.3̅51).

Front

What is the repeating decimal for the fraction 58/165?

Back

The repeating decimal for 58/165 is approximately 0.351515... (or 0.35̅15).

Front

What is the repeating decimal for the fraction 17/99?

Back

The repeating decimal for 17/99 is approximately 0.171717... (or 0.1̅7).