Rational and Irrational Numbers – Terminating and Repeating Decimals

Terminating and Repeating Decimals

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Students learn that a terminating decimal is a decimal that ends. For example, 0.5 and 36.8924 are terminating decimals. Students learn that a repeating decimal is a non-terminating (non-ending) decimal. For example, 0.3333... and 9.257257... are repeating decimals. To indicate that a decimal is repeating, a bar is drawn above the digit or group of digits that repeats. For example, 0.3333... can be written as 0.3 with a bar over the 3. To determine whether a given fraction, such as 4/5, can be written as a terminating or repeating decimal, divide the denominator into the numerator of the fraction. Since 5 divided into 4 is 0.8, 4/5 can be written as a terminating decimal.
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