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Which statement is true when a rational number in fractional form is converted to a decimal?

I. The decimal repeats.
II. The decimal terminates.
A.
neither I nor II
B.
either I or II
C.
II only
D.
I only

1 answer

The statement that is true when a rational number in fractional form is converted to a decimal is:

B. either I or II.

This is because:

  1. A rational number can either have a terminating decimal or a repeating decimal.
  2. If the denominator (in lowest terms) of the fraction has only the prime factors 2 and/or 5, then the decimal representation of the fraction will terminate.
  3. If the denominator has prime factors other than 2 and/or 5, the decimal representation will repeat.

Thus, a rational number can fall into one of those two categories, making option B the correct choice.