Question 295806
Let {{{x=0.7575}}} where the '75's continue on forever



Multiply both sides by 100 to get {{{100x=75.7575}}} where the '75's continue on forever



From here, subtract both sides by 'x' to get {{{100x-x=75.7575-x}}}. Now plug in {{{x=0.7575}}} on the right side to get {{{100x-x=75.7575-0.7575}}}



Now combine like terms: {{{99x=75}}} and then divide both sides by 99 to get {{{x=75/99}}}



Because we made {{{x=0.7575}}} and we found that {{{x=75/99}}} as well, we can say that {{{75/99=0.7575}}} (where the 75's go on forever). Note: you can use your calculator to confirm.