Question

Give the equivalent value of the fraction in decimal form, and then determine if it is a terminating or repeating decimal.

The decimal equivalent of 34/5 is _________ . This is a ______ decimal.

Answer 1

Answer: The decimal equivalent of 34/5 is 6.8. It is a terminating decimal because a fraction will have a terminating decimal representation if its denominator is some product of powers of 2 and powers of 5. Here, the denominator is 5, so the decimal fraction will terminate. 34/5 = 68/10 = 6.8 . . . . . this is a terminating decimal value. If the denominator has any other factor (other than 2 or 5), the decimal representation will repeat. The length of the repeat may be up to n-1 digits, where n is the factor of the denominator that remains after powers of 2 and 5 have been removed. For example, the decimal representation of 1/7 has a 6-digit repeat; 1/19 has an 18-digit repeating decimal representation.

Answer 2

The decimal equivalent of 34/5 is 6.8. It is a terminating decimal.

Explanation:

A fraction will have a terminating decimal representation if its denominator is some product of powers of 2 and powers of 5. Here, the denominator is 5, so the decimal fraction will terminate.

34/5 = 68/10 = 6.8 . . . . . this is a terminating decimal value

_____

If the denominator has any other factor (other than 2 or 5), the decimal representation will repeat. The length of the repeat may be up to n-1 digits, where n is the factor of the denominator that remains after powers of 2 and 5 have been removed. For example, the decimal representation of 1/7 has a 6-digit repeat; 1/19 has an 18-digit repeating decimal representation.