Writing repeating decimals as 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

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

Front

Convert -0.467467467... to a fraction.

Back

-\frac{467}{999}

Front

Convert 0.1\overline{6} to a fraction.

Back

\frac{1}{6}

Front

Convert 4.363636... to a fraction.

Back

\frac{48}{11}

Front

Convert 0.769769769... to a fraction.

Back

\frac{769}{999}

Front

Convert 3.56 to a fraction.

Back

\frac{89}{25}

Front

What is the formula for converting a decimal of the form 0.a\overline{b} to a fraction?

Back

\frac{10a + b}{99} where a is the non-repeating part and b is the repeating part.

Front

What is the significance of the denominator in fractions derived from repeating decimals?

Back

The denominator is often a power of 10 minus 1, reflecting the length of the repeating sequence.

Front

What is the difference between terminating and repeating decimals?

Back

Terminating decimals have a finite number of digits after the decimal point, while repeating decimals have an infinite sequence of digits that repeat.