1. Give an example of a repeating decimal where two digits repeat. Explain why your number is a rational number.
2. Explain why any rational number is either a terminating or repeating decimal.
3. Write two decimals, one repeating and one terminating, with values between 0 and 1. Then write an inequality that shows the relationship between your two decimals.
4. Find the decimal equivalent for the fraction of students with three siblings. (Fraction of students: $$\frac{1}{6}$$).

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).

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