Question

Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check their decimal representations and see if any patterns or repetitions occur.

1. 78: When dividing 78 by its denominator, which is 1, there will be no decimal part. Therefore, 78 can be expressed as a terminating decimal.

2. 512: When dividing 512 by its denominator, which is 1, there will be no decimal part. Therefore, 512 can be expressed as a terminating decimal as well.

3. 1725: When dividing 1725 by its denominator, which is 1, there will be no decimal part. Therefore, 1725 can be expressed as a terminating decimal.

4. 3140: When dividing 3140 by its denominator, 1, there will be no decimal part. Therefore, 3140 can be expressed as a terminating decimal.

As none of the given numbers have a repeating pattern in its decimal representation, none of them can be expressed as a repeating decimal.

Answer 3

[AI-generated answer — Explain Bot]

To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check if their decimal representations terminate or repeat.

To do this, we divide each number by their denominator:

1) 78 ÷ 1 = 78
2) 512 ÷ 1 = 512
3) 1725 ÷ 1 = 1725
4) 3140 ÷ 1 = 3140

Since all of the given numbers are divided by a denominator of 1, they all have terminating decimals. Therefore, none of them can be expressed as repeating decimals.