Question

Write the fraction as a decimal. State whether the decimal is terminating or repeating: 7/20

Answer 1

0.35; terminating

Explanation:

You want to know what the decimal equivalent of 7/20 is, and whether it is terminating or repeating.

Value

Dividing 7 by 20 gives 0.35. That's all.

There are no repeating digits, so this decimal is "terminating."

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Additional comment

The denominator of 7/20 is 20 = 2²·5. Its only factors are 2 and 5, so any decimal with this denominator will be terminating. If the denominator has factors other than 2 or 5, the decimal will be repeating.

For example, 8/21 is a repeating decimal. The factors of its denominator are 3 and 7, not powers of 2 or 5.

`(8)/(21)=0.380952\overline{380952}`

The long division for this is shown in the attachment. It shows you the dividends 80 and 17 show up again as the division progresses. That is what makes the decimal repeat.