Learn Can You Guess What Property Q Must Satisfy

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# Look at several examples of rational number in the form p q ( q ? 0 ) , where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy ?

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

## Answer: q should not be 0 and can be expressed as a power of 2, or 5, or both.

Let's look at the explanation.

**Explanation:**

In every terminating rational number, you will find that the denominator is always a power of 2, or 5, or both.

For example,

1/4 = 1/2^{2}

13/8 = 13/2^{3}

23/125 = 23/5^{3}

15/20 = 15/2^{2} × 5^{1}

All these rational numbers have terminating decimal representations.

### Thus, q should not 0 and can be expressed as a power of 2, or 5, or both.

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