Convert the recurring and noterminating decimals to fraction 2.3455555555

  2111/900

Work Shown:

x = 2.34555555555

100x = 234.555555555

1000x = 2345.555555555

1000x-100x = 2345.555555555-234.555555555

900x = 2111

x = 2111/900

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