Question

Express 1.2333333..... In
ela
form where p and q are co primes.​

Answer 1

1.2333333..... In  form $\dfrac{p}{q}$ = $\dfrac{111}{90}$

where p=111 and q=90 are co primes

Step-by-step explanation:

Let $\textrm{x}=1.2333333$

$\textrm{x}=1.233333.....$$=1.2\overline{3}$

$\Rightarrow 10\textrm{x}=12.\overline{3}$

$\Rightarrow 100\textrm{x}=123.\overline{3}$

$\Rightarrow 100\textrm{x}-10\textrm{x}=123.\overline{3}-12.\overline{3}$

$\Rightarrow 90\textrm{x}=111$

$\Rightarrow \textrm{x}=\dfrac{111}{90}$

So $1.233333.... =\dfrac{111}{90}$

where p=111 and q=90

we know If HCF(a,b) =1 then a,b are co prime

so here  HCF(111,90) =1  

so 111 and 90 are both co prime