Question

2.314 (14 repeating) as a fraction

Answer 1

Step-by-step explanation:

2.3141414...

= 2 + 3/10 + 14/990

= 2 + 311/990

= 2291 / 990

Answer 2

Answer:

Therefore, x =  $\frac{2291}{990}$.

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= $\frac{229.1}{99}$.

x =  $\frac{2291}{990}$.

Therefore, x =  $\frac{2291}{990}$.