Question

Express the following decimal as a rational number.

2.67

Answer 1

Let x = 2.67
Then, x = 2.676767.....       ....(1)
Here, the number of digits recurring is 2, so we multiply both sides of the equation (1) by 100.
∴ 100x = 100 x 2.676767....
= 267.8989.....       ....(2)
On subtracting (1) from (2), we get
99x = 265

∴ x = `(265)/(99)`

∴ 2.67 = `(265)/(99)`