Question

express 0.32
2 is having bar in the form of p upon q

please give accurate answer​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; accurate \: solution...}}}}}$

⋆ Understanding the question: This question says that we have to express ${\sf{0.3\overline{2}}}$ in the form of ${\sf{\dfrac{p}{q}}}$ that is rational number. Let us solve this question!

${\sf{:\implies 0.3\overline{2}}}$

${\sf{:\implies Let \: 0.3\overline{2} \: = x}}$

${\sf{:\implies So, \: x \: = 0.3\overline{2}}}$

~ As we already know that wherever bar is pointed then the term is repeating henceforth,

${\sf{:\implies So, \: x \: = 0.3222222 \dots}}$

${\sf{:\implies x \: = 0.3222222 \dots Eq_{n} \: 1^{st}}}$

~ Now as the bar is on a single digit so we have to multiply the equation 1 by 10. By doing multiplication we get,

${\sf{:\implies x \times 10 \: = 10 \times 0.3222222 \dots}}$

${\sf{:\implies 10x \: = 3.222222 \dots Eq_{n} \: 2^{nd}}}$

~ Now let's subtact equation 1 and equation 2.

${\sf{:\implies 10x \: = 3.222222 \dots}}$

${\sf{:\implies x \: = 0.3222222 \dots}}$

~ By doing subtraction we get,

${\sf{:\implies 9x \: = 2.9}}$

${\sf{:\implies x \: = \dfrac{2.9}{9}}}$

${\sf{:\implies x \: = \dfrac{29}{9 \times 10}}}$

${\sf{:\implies x \: = \dfrac{29}{90}}}$

Henceforth, the given irrational number is expressed in the form of ${\sf{\dfrac{p}{q}}}$ that is rational number!