Question

Which fraction has a repeating decimal as its decimal expansion?

StartFraction 3 Over 19 EndFraction
StartFraction 3 Over 16 EndFraction
StartFraction 3 Over 11 EndFraction
StartFraction 3 Over 8 EndFraction

Answer 1

C

Explanation:

StartFraction 3 Over 11 EndFraction

Answer 2

3/19, 3/11 are repeating decimals

Explanation:

Any fraction with a denominator factor that is something other than 2 or 5 will be a repeating decimal.

`\boxed{(3)/(19)=0.\overline{157894736842105263}}\\\\(3)/(16)=0.1875\\\\\boxed{(3)/(11)=0.\overline{27}}\\\\(3)/(8)=0.375`

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Most calculators will not show the 18-digit repeat of 3/19, since they display fewer digits than that. You have to know that a denominator factor of 19 will result in a repeat that can be as long as 19-1 = 18 digits.