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.
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:
- Let x = 0.52525252...
- Multiply x by 100 (because there are two repeating digits, 52), so 100x = 52.52525252...
- 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
- Solve for x by dividing both sides by 99: x = 52/99
So, the fraction form of 0.52525252... is 52/99.
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