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. For example, 0.333... is a repeating decimal where '3' repeats.

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, subtract the original equation from this new equation, and solve for the variable.

Front

Convert the repeating decimal 0.666... to a fraction.

Back

Front

What is the significance of the bar notation in repeating decimals?

Back

The bar notation indicates which digits repeat. For example, in 0.1̅6, the '6' repeats indefinitely.

Front

Convert the repeating decimal 0.1̅4 to a fraction.

Back

Front

What is the fraction representation of 0.08̅3?

Back

Front

How do you represent a mixed number as a fraction?

Back

A mixed number consists of a whole number and a proper fraction. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator, placing the result over the original denominator.

Front

Convert the mixed number 2 4/9 to an improper fraction.

Back

Front

What is the fraction representation of -0.6̅?

Back

Front

How do you identify the repeating part of a decimal?

Back

The repeating part can be identified by looking for a sequence of digits that appears after a certain point in the decimal. This sequence will continue indefinitely.