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Convert 0.52˙ to a fraction.Give your answer in its simplest form.

Question

Convert 0.52˙ to a fraction.Give your answer in its simplest form.

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Solution

The given number is 0.52525252... and so on, which is a repeating decimal. The decimal part that is repeating is 52.

To convert a repeating decimal into a fraction, we can use the following steps:

  1. Let x = 0.52525252...
  2. Multiply x by 100 (because there are two repeating digits, 52), so 100x = 52.52525252...
  3. Subtract the original equation (step 1) from the new equation (step 2) to get: 100x - x = 52.52525252... - 0.52525252..., which simplifies to 99x = 52
  4. Solve for x by dividing both sides by 99: x = 52/99

So, the fraction form of 0.52525252... is 52/99.

This problem has been solved

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