Question

which of the following rational numbers can be expressed as a repeating decimal: 7/8,5/12,17/25 or 31/40

Answer 1

The rational numbers that can be expressed as repeating decimals are 5/12 and 31/40.

Step-by-step explanation:

Rational numbers can be expressed as repeating decimals when they can't be simplified to a terminating decimal. To determine if a rational number can be expressed as a repeating decimal, we need to determine if the denominator has any prime factors other than 2 and 5. If it does, the decimal representation will be repeating. Let's check each given number:

7/8 = 0.875 (terminating decimal)

5/12 = 0.41666... (repeating decimal)

17/25 = 0.68 (terminating decimal)

31/40 = 0.775 (repeating decimal)

Therefore, the rational numbers that can be expressed as repeating decimals are 5/12 and 31/40.