Question

1. Give an example of a repeating decimal where two digits repeat. Explain why your number is a rational number.

Answer 1

1. A repeating decimal is a decimal number that eventually takes on a repeating pattern of digits after its decimal point that will continue forever. For example, 17.(23)=17.23232323232323....

2. A decimal number that has digits that do not go on forever is called terminating decimal. Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

3. Repeating decimal between 0 and 1: 0.(987)=0.987987987987...

Terminating number between 0 and 1: 0.987

0.(987) >0.987.

4. When dividing 1 by 6 you can get 0.1666666666...=0.1(6).