Answer:
Therefore, x = 2291/990
Step-by-step explanation:
Given : 2.314 (14 repeating) .
To find : Express as a fraction .
Solution : We have given 2.314 (14 repeating) .
Let x = 2.31414141.......
On multiplying both sides by 100
100x = 100 * 2.31414141....
100x = 231.414141......
We can express 231.414141...... in term of x .
100x = 229 .1 + 2.31414141.......
100x = 229.1 +x
On subtracting both sides by x .
100 x -x = 229 .1
99x = 229.1
On dividing both sides by 99
x= 229.1/99
x = 2291/990
Therefore, x = 2291/990
