To determine which rational numbers can be expressed as repeating decimals, we need to check if the denominator can be written as the product of powers of prime numbers that do not include 2 or 5.
1) 78 = 2 * 3 * 13 --> This number can be expressed as a repeating decimal.
2) 512 = 2^9 --> This number cannot be expressed as a repeating decimal.
3) 1725 = 3 * 5^2 * 23 --> This number cannot be expressed as a repeating decimal.
4) 3140 = 2^2 * 5 * 157 --> This number cannot be expressed as a repeating decimal.
Therefore, the rational number 78 can be expressed as a repeating decimal.
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point
1 answer