Which fraction gives a decimal answer whose nonzero digits repeat infinitely many times?

Question

Responses

6
4
6 fourths

8
9
8 ninths

9
8
9 eighths

7
8
7 eighths

Answer 1

To determine which fraction gives a decimal answer with nonzero digits that repeat infinitely, we need to analyze each of the fractions involved to see if their decimal representations are repeating.

Analysis:

1. 6/4 (or 6 fourths):

   • This simplifies to 3/2 which is 1.5. The decimal does not repeat.

2. 8/9 (or 8 ninths):

   • This gives 0.888..., which is a repeating decimal (the "8" repeats).

3. 9/8 (or 9 eighths):

   • This simplifies to 1.125. The decimal does not repeat.

4. 7/8 (or 7 eighths):

   • This gives 0.875. The decimal does not repeat.

Conclusion:

The fraction that gives a decimal answer with nonzero digits repeating infinitely is 8/9 (8 ninths).