Question

express 0.33bar in from of p/q​

Answer 1

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⋆ It is given that we have to express the given number in a rational number that is in the form of ${\sf{\dfrac{p}{q}}}$ The given number is ${\sf{0.\overline{33}}}$ Let us solve this question!

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~ We have to express the given number in the form of ${\sf{\dfrac{p}{q}}}$

${\sf{:\implies 0.\overline{33}}}$

${\sf{:\implies Let \: 0.\overline{33} \: = x}}$

${\sf{:\implies Let \: x \: = 0.\overline{33}}}$

~ Now let's carry on!

${\sf{:\implies Therefore, \: x \: = 0.333333 \dots \: Equation \: 1}}$

~ Now we have to multiply ...Equation 1 from 100. (Why with 100? Because bar is on two digits!)

${\sf{:\implies Therefore, \: x \times 100 \: = 0.333333 \dots 100}}$

${\sf{:\implies 100x \: = 33.333333 \dots \: Equation \: 2}}$

~ Now we have to subtract ...Equation 1 from ...Equation 2

${\sf{:\implies 100x \: = 33.333333}}$

${\sf{:\implies x \: = 0.333333}}$

~ Subtracting we get the following!

${\sf{:\implies 99x \: = 33}}$

~ Now let's carry on!!

${\sf{:\implies x \: = \dfrac{33}{99}}}$

${\sf{:\implies x \: = \cancel{\dfrac{33}{99}}}}$

${\sf{:\implies x \: = \dfrac{1}{3}}}$

Henceforth, expressed!!!

${\large{\pmb{\sf{\underline{KnowlEdge...}}}}}$

Rational number: Rational number are those numbers which can be written in the form of ${\sf{\dfrac{p}{q}}}$ where q ≠ 0 i.e., q is not equal to zero. Some example of rational number are ${\sf{\dfrac{23}{9} \: , \dfrac{777}{44432}}}$

Irrational number: Irrational number are the inverse of rational numbers. These numbers can't be written in the form of ${\sf{\dfrac{p}{q}}}$ The bestest example for irrational numbes are ${\sf{\pi}}$ and ${\sf{\sqrt{}}}$