Question

. Convert 12.3454545… into rational fraction

Answer 1

Step-by-step explanation:

Step I: Let x = 12.34545…

Step II: The repeating digits of the given decimal fraction are ‘45’.

Step III: Now we need to transfer repeating digits to the left of the decimal point. To do so, we need to multiply the original number by 1000. So,

1000x = 12345.4545

Step IV: Now we have to shift the repeating digits to the right of the decimal point. To do so we have to multiply the original number by 10. So,

              10x = 123.4545

Step V: Two equations are as:

            1000x = 12345.4545, and

        ⟹    10x = 123.4545

Now we have to perform the subtraction on both sides of the equation to maintain the equality.

           1000x – 10x = 12345.4545 – 123.4545

     ⟹              990x = 12222

      ⟹                   x = 12222990

      ⟹                   x = 1358110

      ⟹                  x = 67955

   Hence, the required rational fraction is 67955.

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