Question 130094

{{{x=0.0101010101}}} Set the decimal value equal to x. Let's call this Equation 1



{{{100*x=100*0.0101010101}}} Multiply both sides by 100



{{{100x=1.0101010101}}} Multiply (or move the decimal 2 places to the right on both sides). Let's call this Equation 2





{{{99x=1}}} Now subtract Equation 2 from  Equation 1 by subtracting the left side terms {{{100x-x=99x}}} and the right side terms {{{1.0101010101-0.0101010101=1}}}






{{{x=1/99}}} Now divide both sides by 99 to isolate x





So the decimal number  {{{0.0101010101}}} is the fraction  {{{1/99}}}



In other words, {{{0.0101010101=1/99}}}