How to convert a recurring decimal to fraction
Answers
Answer:
Let x equal the repeating decimal you are trying to convert to a fraction. Examine the repeating decimal to find the repeating digit(s). Place the repeating digit(s) to the left of the decimal point. Place the repeating digit(s) to the right of the decimal point.
Answer:
Write 0.77.. as a fraction in its lowest terms.
Our first step is to form a simple equation where x=0.77... By multiplying both sides by 10 we can obtain another equation with 10x=7.77... Now we eliminate the recurring part of the decimal by subtracting x from 10x.
x10x9xx=0.77..=7.77..=7=79
So we have our answer 0.77...=79.
The important part to remember is to get two equations in x where the recurring part after the decimal point is exactly the same.
Step-by-step explanation;
A recurring decimal is a number which keeps repeating forever after the decimal point. The first recurring decimal most people meet is 13=0.33... In most books a recurring decimal is represented by placing a dot above the number or numbers that repeat.
All recurring decimals can be represented as fractions. To find this fraction we need to generate two equations which have the same repeating part and subtracting one from the other to eliminate it.