You are given a fraction in simplest form where the numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal. Which numbers from 1 to 10 could be the denominator?

Please help!

You could easily do that yourself, with a pencil, and about the same amount of time it took you to post the question here.
If you go through and try them . . . 1/1, 1/2, 1/3, 1/4, 1/5 . . . etc., you'll find that the thirds, sixths, sevenths, and ninths produce repeating decimals. The oneths, tooths, fourths, fifths, eighths, and tenths don't.

Answered by AL2006 | 2024-06-10

The correct answer is:
3, 6, 7, 9
Explanation :
If your denominator was 1, you would have whole numbers, not repeating decimals.
If your denominator was 2, you would have halves. These do not repeat.
If your denominator was 4, you would have 0.25 or 0.75.
If your denominator was 5, you would have 0.2, 0.4, 0.6, or 0.8.
If your denominator was 8, you would have 0.125, 0.375, 0.625, or 0.875.
If your denominator was 10, you would have 0.1, 0.3, 0.7, or 0.9.
However, if your denominator is 3, you would have repeating 3's or 6's. If your denominator was 6, you would have a 1 with a repeating 6 or an 8 with repeating 3's. If your denominator was 7, you would have repeating 0.142857, repeating 0.285714, repeating 0.428571, repeating 0.571428, repeating 0.714285, or repeating 0.857142. If your denominator was 9, you would have repeating 1's, 2's, 4's, 5's, 7's, or 8's.

Answered by MsEHolt | 2024-06-11

The denominators from 1 to 10 that result in repeating decimals when expressed as fractions are 3, 6, 7, and 9. Other denominators like 1, 2, 4, 5, 8, and 10 do not produce repeating decimals. Therefore, the answer is 3, 6, 7, and 9.
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Answered by AL2006 | 2024-09-30