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Put the repeating digits over the same number of 9s as there are repeating digits; then simplify.

examples

  • 0.333333....
There is 1 repeating digit (3), so one 9 in the denominator:

0.3333.... = 3/9 = 1/3

  • 0.14285714285714....
There are 6 repeating digits (142857) so six 9s in the denominator:

0.14285714285714... = 142857/999999 = 1/7

  • 5.6666....
There is 1 repeating digit (6), so one 9 in the denominator:

5.6666... = 5 + 0.6666....

= 5 + 6/9

= 5 + 2/3

= 52/3

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Q: How do you convert repeating decimal into a mixed number?
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