Terminating vs. Repeating Decimals

Front

What is a terminating decimal?

Back

A terminating decimal is a decimal number that has a finite number of digits after the decimal point.

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal number that has one or more digits that repeat infinitely after the decimal point.

Front

How can you identify if a fraction will result in a terminating decimal?

Back

A fraction will result in a terminating decimal if its denominator (in simplest form) has only the prime factors 2 and/or 5.

Front

What is the overbar notation for a repeating decimal?

Back

Overbar notation is a way to represent repeating decimals by placing a line (overbar) over the digits that repeat.

Front

Convert the decimal 0.333... to fraction form.

Back

0.333... = 1/3.

Front

What is the decimal representation of 1/4?

Back

1/4 = 0.25, which is a terminating decimal.

Front

What is the decimal representation of 1/3?

Back

1/3 = 0.333..., which is a repeating decimal.

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 to shift the decimal point, and then solve for the variable.

Front

What is the significance of the number of digits in the repeating part of a decimal?

Back

The number of digits in the repeating part determines the denominator of the fraction when converting the decimal to a fraction.

Front

Can a decimal be both terminating and repeating?

Back

No, a decimal cannot be both terminating and repeating; it can only be one or the other.