Answer: 2111/900
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Work Shown:
x = 2.34555555555
100x = 234.555555555
1000x = 2345.555555555
1000x-100x = 2345.555555555-234.555555555
900x = 2111
x = 2111/900
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Notes:
- In step 2, I multiplied both sides by 100 to move the decimal point two spots to the right. Step 3 is a similar idea, but the decimal point moves 3 spots to the right. This is done so that we have the infinite string of '555...' be after the decimal point.
- In step 4, the terms subtract, and in the next step, the infinite string of '555...' cancels out. So that's why steps 2 and 3 happened to help set this up.
- You can use your calculator to confirm that 2111/900 = 2.3455555...
- Your calculator is likely to round that last 5 into a 6.
- The answer in bold is an improper fraction. If you need to convert to a mixed number, then that value would be 2 & 311/900
