How do you put .81 repeating in fraction form?

Answer 1

9/11

81 = 9 x 9

9 x 11 = 99

so 0.818181 x 11/9 = 0.999999 = nearly 1

then reversing the fraction

0.818181 = 9/11

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To convert a recurring decimal to a fraction:

1) Multiply the decimal by 10 to the power of the number of repeating digits.

2) Subtract the original decimal from this

3) put the result of the subtraction over the power of 10 in step 1 less 1

4) Simplify

For 0.818181... there are 2 repeating digits, therefore power of 10 is 2, ie 10² = 100

0.818181... × 100 = 81.818181...

Subtracting original gives: 81.818181... - 0.818181... = 81

Put over 100 -1 gives: 81/(100-1) = 81/99

Simplify: 81/99 = (9×9)/(9×11) = 9/11