Name: Conversion of Decimals to Fractions
Uploaded: 2019-07-19
Duration: 3 min 37 s
Description: In this video, we will learn the concept of converting decimal numbers to fractional values and how they are related to each other.

Question

Convert the decimals $0 . \bar{9}, 14 . \bar{5}$ and $1.2 \bar{4}$ to rational form. Can you find any easy method other than formal method?

Accepted Answer

Let $x = 0 . \bar{9}$

$\Rightarrow x = 0.999 . . . .$ _________ $(i)$

The periodicity of the decimal is one.

Multiplying both sides of equation $(i)$ by $10$ , we get,

$10 \times x = 10 \times 0.9999 . . . . . . . .$

$\Rightarrow 10 x = 9.99 . . . . . .$ _________ $(ii)$

Subtracting equation $(i)$ from $(ii)$

$10 x - x = (9.99 . . . . .) - (0.99 . . . . . .)$

$\Rightarrow 9 x = 9$

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

$\Rightarrow x = 1$

The rational form of $0 . \bar{9}$ is $1$ .

Let $y = 14 . \bar{5}$

$\Rightarrow y = 14.555 . . . . . . . .$ ________ $(iii)$

The periodicity of the decimal is one.

Multiplying both sides of equation $(iii)$ by $10$ , we get,

$10 \times y = 10 \times 14.55555 . . . . . . . .$

$\Rightarrow 10 y = 145.555555 . . . . . .$ _________ $(iv)$

Subtracting equation $(iii)$ from $(iv)$

$10 y - y = (145.5555 . . . . .) - (14.5555 . . . . . .)$

$\Rightarrow 9 y = 131$

$\Rightarrow y = \frac{131}{9}$

The rational form of $14 . \bar{5}$ is $\frac{131}{9}$ .

Let $m = 1.2 \bar{4}$

$\Rightarrow m = 1.2444 . . . .$ ________ $(v)$

The periodicity of the decimal is one.

Multiplying both sides of equation $(v)$ by $10$ , we get,

$10 \times m = 10 \times 1.24 . . . . . . . .$

$\Rightarrow 10 m = 12.4444 . . . . . .$ _________ $(vi)$

Subtracting equation $(v)$ from $(vi)$

$10 m - m = (12.4444 . . . . .) - (1.24444 . . . . . .)$

$\Rightarrow 9 m = 11.2$

$\Rightarrow m = \frac{11.2}{9}$

$\Rightarrow m = \frac{11.2 \times 10}{9 \times 10}$

$\Rightarrow m = \frac{112}{90}$

$\Rightarrow m = \frac{56}{45}$

The rational form of $1.2 \bar{4}$ is $\frac{56}{45}$ .

No, there is no other easier method other than the formal method.

Convert the decimals $0 . \bar{9}, 14 . \bar{5}$ and $1.2 \bar{4}$ to rational form. Can you find any easy method other than formal method?

Important Questions on Rational Numbers

Learn and Prepare for any exam you want !

Convert the decimals 0.9¯, 14.5¯ and 1.24¯ to rational form. Can you find any easy method other than formal method?

Important Questions on Rational Numbers

Learn and Prepare for any exam you want !

Convert the decimals $0 . \bar{9}, 14 . \bar{5}$ and $1.2 \bar{4}$ to rational form. Can you find any easy method other than formal method?