Question

Express 3.75bar in p/q form where p and q are integers. (note-3.75 has a bar on top it is a repeating number) ​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

⋆ Some basic concept's:

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 ${\sf{\sqrt{}}}$

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⋆ Given that: We have to express ${\sf{3.\overline{75}}}$ in the form of ${\sf{\dfrac{p}{q}}}$ that is rational number, where p and q are integers. Note: ${\sf{3.\overline{75}}}$ , the overline in bar and it denotes irrational number that is repeating!

${\sf{:\implies 3.\overline{75}}}$

${\sf{:\implies{Let \: 3.\overline{75} \: = x}}}$

${\sf{:\implies{So \: x \: = 3.\overline{75}}}}$

${\sf{:\implies{x \: = 3.75757575 \dots \dots Equation \: 1^{st}}}}$

Now let's multiply 100 by Equation 1st. Afterwards we get,

${\sf{:\implies 100 \times x \: = 100 \times 3.75757575 \dots \dots}}$

${\sf{:\implies 100x \: = 375.757575 \dots \dots Equation \: 2^{nd}}}$

Now let's subtact Equation 1st and equation 2nd

${\sf{:\implies 100x \: = 375.757575 \dots \dots}}$

${\sf{:\implies x \: = 3.75757575 \dots \dots}}$

${\sf{:\implies 99x \: = 372.000 \dots \dots}}$

${\sf{:\implies x \: = \dfrac{372}{99}}}$

Henceforth, expressed!!

Answer 2

Step-by-step explanation:

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