SOLUTION: Express 1.234 (with the 34 recurring) as a fraction in simplest form.

Question 1108765: Express 1.234 (with the 34 recurring) as a fraction in simplest form.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Ignore the whole number part and convert the repeating decimal; then add the whole number part back into the answer.

Slow, formal algebraic method....

Call the number x. Then, since 2 digits are repeating, multiply x by 100 and subtract x from the result. The repeating digits will line up and are cancelled by the subtraction.

Then the final answer is the mixed number 1 116/495; or, if an improper fraction answer is asked for, .

Shortcut....

Write out on paper the process shown above to see how this shortcut works....

The denominator of the fraction in unsimplified form is 990, because there are two digits that repeat and one digit that does not repeat. In general, the denominator is one 9 for each repeating digit followed by one 0 for each non-repeating digit.

The numerator of the fraction is (the non-repeating digits plus one cycle of the repeating digits) minus (the non-repeating digits) -- in your example, "234 - 2".

So without going through all the formal algebra shown earlier, you can just write down the (unsimplified) answer:

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