Recurring decimals to fractions

Recurring decimals to fractions

1. What is 0.454545454545454545(recurring) as a fraction?

   • 1. Write it as x = 0.4545454545...
     • 2. Multiply the decimal by a power of 10 that leaves the bit after the decimal the same
       • (x100) 100x = 45.454545...
         • 3. Subtract the original number from the new one
           • 99x = 45.
             • Divide by the number of x
               • 45 ÷ 99 = 45/99
                 • Cancel the fraction
                   • 5/11

2. 0.238383838...

   • x = 0.238383838
     • You can't get it so that the number is the same on both sides because of the 2.
     • 1000x = 238.3838383838
       • 10x = 2.38383838
         • 990x = 236
           • x = 236/990
             • 118/445