Question

Which of the following numbers can be expressed as repeating decimals?

4/7, 2/5, 7/8, 4/9
A. 7 over 8 and 4 over 9
B. 4 over 7 and 2 over 5
C. 4 over 7 and 4 over 9
D. 2 over 5 and 7 over 8

Answer 1

The fractions 4/7 and 4/9 can be expressed as repeating decimals because their denominators are not a product of only the prime factors 2 and/or 5. Hence, the correct answer is option C.

Step-by-step explanation:

The numbers that can be expressed as repeating decimals are those whose denominators, when in their simplest form, are a product of only the prime factors 2 and/or 5. Therefore, to determine which options given are repeating decimals, examine each fraction.

• 4/7: The denominator is 7, which is not a product of only 2's or 5's. Therefore, 4/7 is a repeating decimal.
• 2/5: The denominator is 5, which is a product of only 5. Therefore, 2/5 has a terminating decimal.
• 7/8: The denominator is 8, which is 2³ (a product of only 2's). Therefore, 7/8 has a terminating decimal.
• 4/9: The denominator is 9, which is not a product of only 2's or 5's. Therefore, 4/9 is a repeating decimal.

So, the numbers that can be expressed as repeating decimals are 4/7 and 4/9.

The correct answer to the question is C. 4 over 7 and 4 over 9.