Question

Express 2.4178 (178 is repeating) in the form of p/q ?

Answer 1

Solutions 

A fraction is a part of a whole. We call the top number the Numerator, it is the number of parts we have.

We call the bottom number the Denominator, it is the number of parts the whole is divided into. Numerator / Denominator. 

Calculations 

To solve the problem lets use the variable (x). A symbol for a number we don't know yet is called a variable. It is usually a letter . Example x,y,z,etc.... . 

let x be 2.4178 
x= 2.4178(bar on 178)

Our next step is to multiply both the sides by 10.

10x = 24.178(bar on 178) {1}

Now multiply both the sides by 1000

10000x = 24178.178 {2}

Lets subtract {2}- {1}

9990x = 24154 ..

x= 24154 /9990

Simplify x= 24154 /9990 

x = 12077 / 4995 

Answer 2

Let x=2.4178178...--------(1)
Here,periodicity is 3
So we should multiply 'x' with 1000
⇒ 1000×x=1000×2.4178178....
⇒1000x=2417.8178178...--------(2)
(2)-(1)=
1000x-x=2417.8178178....-2.4178178.....
⇒999x=2415.40000.....
⇒999x=24154/10
⇒x=24154/(10×999)
⇒x=24154/9990
⇒x=12077/4995
∴The p/q form of 2.4178.....is 24154/9990 or 12077/4995