Rational Numbers in Different Forms Practice

Question

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

Answer 1

To determine which of the given rational numbers can be expressed as a repeating decimal, we need to consider their denominator when expressed in simplest form. A rational number will have a repeating decimal if, when reduced to its simplest form, the denominator has prime factors other than 2 and 5.

1. 78: It's a whole number, so it can be expressed as a decimal: 78.0 (terminating).
2. 512: It's also a whole number: 512.0 (terminating).
3. 1725: Again, it's a whole number: 1725.0 (terminating).
4. 3140: Yet another whole number: 3140.0 (terminating).

None of the above whole numbers have a denominator after simplification, so they are not expressed as repeating decimals.

Since all provided options are integers and thus will convert to terminating decimals in decimal form, none of these numbers are repeating decimals.

The answer is none of the options listed can be expressed as a repeating decimal; all are terminating when expressed in decimal form.

Answer 2

anwser

Answer 3

None of the given rational numbers (78, 512, 1725, and 3140) can be expressed as a repeating decimal; all of them are terminating decimals. Therefore, the answer is:

None of the options can be a repeating decimal.

If you're looking for a specific format in terms of repeating decimals, you would need to provide other examples that include numbers that do not simplify to only involve the primes 2 and 5.