Question

Convert 0.27 (27 with ¯¯¯¯¯ on top)
to a rational number in simplest form.(1 point)
Responses

27/100

Start Fraction 27 over 100 end fraction

1/27

Start Fraction 1 over 27 end fraction

3/11

Start Fraction 3 over 11 end fraction

27/99

Start Fraction 27 over 99 end fraction
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Answer 1

Let x = 0.\overline{27}. Then 100x = 27.\overline{27}. Subtract: 100x − x = 27 ⇒ 99x = 27 ⇒ x = 27/99 = 3/11.

Answer: 3/11.