To determine whether a rational number can be expressed as a repeating decimal, we need to check the denominator for factors other than 2 and 5.
The prime factorization of 8 is $2^3$, which means 8 has factors of 2, but no factors of 5. Therefore, 7/8 cannot be expressed as a repeating decimal.
The prime factorization of 12 is $2^2\cdot3$, which means 12 has factors of 2 and 3, but no factors of 5. Therefore, 5/12 cannot be expressed as a repeating decimal.
The prime factorization of 25 is $5^2$, which means 25 has factors of 5, but no factors of 2. Therefore, 17/25 can be expressed as a repeating decimal.
The prime factorization of 40 is $2^3\cdot5$, which means 40 has factors of 2 and 5. Therefore, 31/40 cannot be expressed as a repeating decimal.
Therefore, the rational numbers that can be expressed as a repeating decimal are 7/8 and 31/40
Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40? (1 point)
1 answer
1 answer