Question

2)
Express the following recurring decimals as
a rational number.
i)2.35(bar on 5)​

Answer 1

Answer:

X=2.3555...

10X= 23.55555 be equation 2

100X=235.5555 be equation 3

Finding the difference between equation 3 and equation 2

90X= 212

X= 212÷90 is the rational number.

Answer 2

The number in rational form is $2.3\bar{5}=\frac{106}{45}$

Step-by-step explanation:

Given : Decimal 2.35(bar on 5)​.

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

Solution :

Let the number be $x=2.3\bar{5}$

$x=2.35555...$ ....(1)

Multiply both side by 10,

$10x=23.5555...$ ....(2)

Subtract (1) and (2),

$10x-x=(23.5555)-(2.3555)...$

$9x=21.2$

$x=\frac{21.2}{9}$

$x=\frac{212}{90}$

$x=\frac{106}{45}$

Therefore, the number in rational form is $2.3\bar{5}=\frac{106}{45}$

#Learn more

Express 0.361 recurring decimal into fraction

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