Question

Express the following decimal as a rational number.

0.7

Answer 1

Let x = 0.7
Then, x = 0.7777.....        ....(1)
Here, the number of digits recurring is only 1, so we multiply both sides of the equation (1) by 10.
∴ 10x = 10 x 0.7777....
=7.777.....       ....(2)
On subtracting (1) from (2), we get
9x = 7

∴ x = `(7)/(9)`

∴ 0.7 = `(7)/(9)`