Express each of the following in p/q form

1.	Express each of the following in p/q form
Answer» Let us consider the number as (x) So , accordingly ; the equation becomes : $\tt{ x \implies 3.88888... or \: 3.\bar{8}}$ -- (1) The number after 3 is 8 and it is only getting repeated ; so we can conclude that the periodicity is 1 . So , we will multiply both the sides of the equation by 10 as 10 is the only number that has 1 zero after 1 . MULTIPLYING both the sides by 10 gives us : $\tt{ 10x \implies 38.8888....}$ --(2) Now , we will Subtract equation (1) from (2). $\tt{ 10 x - x \implies 38.8888...(-)3.888....}$ $\tt{ 9x \implies 35}$ $\large{\boxed{\tt{ x \implies \dfrac{35}{9}}}}$ Supplementary INFORMATION : The numbers which can be expressed in p by q FORM where p and q are integers and q is not equal to zero and known as rational numbers. They are either terminating or recurring. Eg : 1/2 , -5/7 The numbers which cannot be expressed in p by q form are known as irrational numbers. They are NON terminating and non recurring. Eg : √2 , √3 , √7 , 1.373924937390183

Answer»

Let us consider the number as (x)

So , accordingly ; the equation becomes :

$\tt{ x \implies 3.88888... or \: 3.\bar{8}}$ -- (1)

The number after 3 is 8 and it is only getting repeated ; so we can conclude that the periodicity is 1 .

So , we will multiply both the sides of the equation by 10 as 10 is the only number that has 1 zero after 1 .

MULTIPLYING both the sides by 10 gives us :

$\tt{ 10x \implies 38.8888....}$ --(2)

Now , we will Subtract equation (1) from (2).

$\tt{ 10 x - x \implies 38.8888...(-)3.888....}$

$\tt{ 9x \implies 35}$

$\large{\boxed{\tt{ x \implies \dfrac{35}{9}}}}$

The numbers which can be expressed in p by q FORM where p and q are integers and q is not equal to zero and known as rational numbers. They are either terminating or recurring.
Eg : 1/2 , -5/7

The numbers which cannot be expressed in p by q form are known as irrational numbers. They are NON terminating and non recurring.
Eg : √2 , √3 , √7 , 1.373924937390183

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