Math 8.2.B

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. For example, 0.75 and 2.5 are terminating decimals.

Front

What is a non-terminating decimal?

Back

A non-terminating decimal is a decimal number that continues infinitely without repeating. For example, 1/3 = 0.333... is a non-terminating decimal.

Front

Which fractions result in terminating decimals?

Back

Fractions that have denominators that are powers of 10 (like 10, 100, 1000) or can be simplified to such forms result in terminating decimals.

Front

Which fractions result in non-terminating decimals?

Back

Fractions that have prime factors in the denominator other than 2 or 5 result in non-terminating decimals. For example, 1/3 and 4/7.

Front

What is the decimal representation of 1/2?

Back

1/2 = 0.5, which is a terminating decimal.

Front

What is the decimal representation of 4/5?

Back

4/5 = 0.8, which is a terminating decimal.

Front

What is the decimal representation of 4/7?

Back

4/7 = 0.571428..., which is a non-terminating decimal.

Front

How can you determine if a fraction will terminate?

Back

To determine if a fraction will terminate, factor the denominator after simplifying the fraction. If the only prime factors are 2 and/or 5, it will terminate.

Front

What is the significance of the denominator in determining decimal types?

Back

The denominator's prime factorization determines whether a fraction's decimal representation is terminating or non-terminating.

Front

Give an example of a fraction that terminates and explain why.

Back

1/4 = 0.25. It terminates because the denominator (4) can be expressed as 2^2, which is a power of 2.