Question

express the following recurring decimals as a rational number : 2.4 (bar on 4)​

Answer 1

The required rational number form is $2.\bar{4}=\frac{22}{9}$

Step-by-step explanation:

Given : Expression $2.\bar{4}$

To find : Express the following recurring decimals as a rational number?

Solution :

Let $x=2.44444$ ....(1)

Multiply both side by 10,

$10x=24.44444...$ .....(2)

Subtract (1) and (2),

$10x-x=(24.444...)-(2.4444...)$

$9x=22$

$x=\frac{22}{9}$

The required rational number form is $2.\bar{4}=\frac{22}{9}$

#Learn more

Express the following recurring decimals as  a rational number.

i)2.35(bar on 5)​

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