Terminating VS. Repeating

Front

What is a rational number?

Back

A rational number can be written as a fraction, where both the numerator and denominator are integers.

Front

What is an irrational number?

Back

An irrational number cannot be written as a fraction; its decimal representation is non-terminating and non-repeating.

Front

Convert the decimal 0.75 into a fraction.

Back

0.75 = \frac{3}{4}.

Front

What is the decimal representation of \frac{1}{2}?

Back

\frac{1}{2} = 0.5.

Front

What does it mean for a decimal to be terminating?

Back

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

Front

What does it mean for a decimal to be repeating?

Back

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

Front

Convert the repeating decimal 0.333... into a fraction.

Back

0.333... = \frac{1}{3}.

Front

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

Back

0.666... = \frac{2}{3}.

Front

What is the decimal representation of \frac{3}{11}?

Back

\frac{3}{11} = 0.272727... (repeating).

Front

How do you convert a repeating decimal to a fraction?

Back

Let x = the repeating decimal, multiply by a power of 10 to shift the decimal, then subtract to eliminate the repeating part.