Question

Express 0.361 recurring as a fraction. (only the 61 recurs)

Answer 1

9514 1404 393

Answer:

  179/495

Step-by-step explanation:

When the repeating decimal starts at the decimal point, the repeating digits can be turned into a fraction by putting them over the same number of 9s. That is, 0.61616161... is equivalent to 61/99.

Here, the repeating part is 1/10 that value, so is 61/990. This is added to the non-repeating part, which is 0.3 = 3/10.

Then the entire decimal is ...

  0.361_61 = 3/10 + 61/990 = (297 +61)/990 = 358/990 = 179/495