Question

express the following recurring decimal as a rational number 51.02( bar on 2)​

Answer 1

Given:

A number with recurring decimal = 51.0222222........

To find:

To convert the number with recurring decimal into a rational number.

Solution:

Let x = 51.022222...........

Multiply by 10 on both the sides,

10x = 510.22222.......... (1)

Multiply by 100 on both the sides,

100x = 5102.22222........... (2)

Now subtract equation (1) from equation (2),

100x = 5102.2222222........

 10x =  510.22222222........

90x = 4592.0

    x = $\frac{4592}{90}$

Therefore, rational number will be $\frac{4592}{90}$.