Write the recurring decimal 0.0755... as a fraction in its lowest terms

The first step is to write x=0.0755... For this question the number that is recurring here is the 555…so what we want is to get two equations with the same recurring part after the decimal point. By multiplying x=0.0755 by 100, we get 100x=7.555… This is our first equation. To get the second equation, we multiply x=0.755.. by 1000 so we get 1000x=75.555. This is our second equation As you can see both equations have the same recurring part. The next step is to subtract the two equations from each other. It doesn’t matter which equation is on the top or the bottom as two negatives cancel each other out but it’s probably easier for you to work with positive numbers. I have put the bigger number on the top so I can work with positive number. Make sure you’re subtracting both sides of the equal signs when you do this step. 1000x=75.555… ② -(100x=7.555…) ① --------------------- 900x=68 Then to find x, you divide by 900 so you get x=68/900=0.07555. So your answer should be 68/900