Question

Express 5.123333...... in p/q form where p and q are co primes

Answer 1

5.123333...... in p/q form =$\dfrac{4611}{900}$

where p=4611 and q =900 are co primes

Step-by-step explanation:

Let $\textrm{x}=5.123333........$

We can write $5.123333......=5.12\overline{3}$

So  $\textrm{x}=5.12\overline{3}$

$\Rightarrow 10\textrm{x}=51.2\overline{3}$

$\Rightarrow 100\textrm{x}=512.\overline{3}$         ................equ(1)

$\Rightarrow 1000\textrm{x}=5123.\overline{3}$       .................equ(2)

As we know $.3333.....=.\overline{3}$

so subtracting equ(1) from equ(2) we get

$1000\textrm{x}-100\textrm{x}=5123.\overline{3}-512.\overline{3}$

$900\textrm{x}=4611$

$\textrm{x}=\dfrac{4611}{900}$

As we know If HCF of two numbers is 1 then both are co prime.

In this case HCF(4611,900)=1

Therefore  $5.123333.......=5.12\overline{3}=\dfrac{4611}{900}$