Question

express each of the following as a fraction in simplest form 3.14

Answer 1

x=3.1414 _ 1eq
*100
100x= 314.1414_2eq
subtract eq 1 from2
100x=314.1414 - x=3.1414
99 x=311.0
x= 311/99

Answer 2

Let x = 3.14⁻ (bar)

∴ x = 3.1414.....                     .......... (1)

We have to find the value of 3.14⁻ (bar) as a fraction in simplest form.

Solution:

Multiplying equation (1) by 100, we get

100(x) = 100(3.1414..... )  

⇒ 100x = 314.1414.....            .......... (2)

On subtracting (1) from (2), we get

100x - x = 314.1414..... - 3.1414.....  

⇒ 99x = 311

Dividing both sides by 99, we get

$\dfrac{99x}{99x}$ = $\dfrac{311}{99}$

⇒ x = $\dfrac{311}{99}$

∴ 3.14⁻ (bar) as a fraction in simplest form x = $\dfrac{311}{99}$

Thus, the value of 3.14⁻ (bar) as a fraction in simplest form is equal to" $\dfrac{311}{99}$".