How to convert 2.43 in ​​​​p/q ​​form ?

Question

How to convert 2.43 in \(\frac{p}{q}\) form ?

Answer 1

Let x = 2.43

 In 2.43, the number 4 on the right side of the decimal point is not recurring. 

So, in order to get only recurring digits on the right side of the decimal point, we will multiply 2.43 by 10. 

∴ 10x = 24.3 …(i) 

∴ 10x = 24.333… 

Here, digit 3 is the only recurring digit. Thus, by

multiplying both sides by 10, 100x = 243.333… 

∴ 100x= 243.3 …(ii)

 Subtracting (i) from (ii), 

100x – 10x = 243.3 – 24.3 

∴ 90x = 219