Question

Express : 2.015bar in the p/q form, where p and q are integers and q not equal to zero(15 has the bar)

Answer 1

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➝ $\rm\:Let\:x=2.0\overline{15}$

⸕ [ multiplying by 10 in both side ]

$\rm\rightarrow\:x\times\:10=2.0\overline{15}\times\:10$

$\rm\rightarrow\:10x=20.\overline{15}\:.............(i)$

⸕ [ multiplying by 100 in both side ]

$\rm\rightarrow\:10x\times\:100=20.\overline{15}\times\:100$

$\rm\rightarrow\:1000x=2015.\overline{15}\:............(ii)$

⸕ [ Subtracting eq (i) from eq (ii) ]

$\rm\:1000x-10x=2015.\overline{15}-20.\overline{15}$

$\rm\rightarrow\:990x=1995$

$\rm\rightarrow\:x=\dfrac{\cancel{1995}}{\cancel{990}}$

$\rm\rightarrow\:x=\dfrac{133}{66}$

$\underbrace{\bf\:More\:Information}$

➝ Rational numbers :- The number of the form p/q where p and q are integers and q ≠ 0 are called rational number.

➝ Rational numbers in decimal :- Every rational number when expressed in decimal form is expressible either in terminating or in nonterminating repeating decimal form.

Answer 2

Answer

STEP By STEP

2.015

let us consider 2.015 =x. (1)

x= 2.015015....

Now multiply both sides by 1000

1000x= 2015.015015....(2)

Subtract equation (2) from equation (1)

1000x=. 2015.015015....

x. -.2.015015....

_______________________________

999x. =. 2013

x= 2013/999

2.015 = 2013/ 999

2013/999 Ans.