EXPRESS THE FOLLOWING IN THW FORM P/Q WHEE P AND Q ARE INTEGER ND Q≠0
a.0.6bar
b.0.47bar
c.0.001bar
PROPER ANSWER WITH PROPER EXPLANATION...
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Answers
Here is your answer,
1. 0.6
Let us assume that x=0.6= 0.6666............------> (1)
Now, we need to Multiply equation (1) with 10
10x = 10×( 0.666...)
10x=6.666...
Subtracting equation(2) from equation(1)
10x-x=6.6666.... - 0.6666...
9x = 6
x= 9/6 = 2/3
2. 0.47 = 0.4777777----> (1)
Now we need to multiply with equation (1) with 10
10x = 10 × (0.47777)...
10x= 4.7777....
Now we need to subtract equation (2) from equation (1)
10x-x = 4.7777...- 0.47777.....
9x = 4.3000
x= 4.3 /9
Therefore x = 43/90
3) 0.001
Let us assume that x= 0.001 = 0.001001......
Now let us multiply equation with 1000
1000 x = 1000 × ( 0.001001...)
Now we need to subtract (2) equation (1) equation
1000x - x = 1.001001...- 0.001001...
999x = 1
x = 1/999
ANSWER:-------
A. given :- 0.66666666...
let x be 0.66666666... --------(1)
multiply both sides by 10.
⇒ 10 * x = 10 * 0.66666666...
⇒ 10x = 6.66666666... ---------(2)
subtract (1) from (2)
⇒ 10x - x = 6.66666666... - 0.666666666...
⇒ 9x = 6
⇒ x = 6/9
⇒ x = 2/3
B. given :- 0.4747474747...
let x be 0.4747474747... --------(1)
multiply both sides by 100.
⇒ 100 * x = 100 * 0.4747474747...
⇒ 100x = 47.4747474747... ---------(2)
subtract (1) from (2)
⇒ 100x - x = 47.4747474747... - 0.4747474747...
⇒ 99x = 47
⇒ x = 47/99
C. given :- 0001001001...
let x be 0.001001001... --------(1)
multiply both sides by 1000.
⇒ 1000 * x = 1000 * 0.001001001...
⇒ 1000x = 1.001001001... ---------(2)
subtract (1) from (2)
⇒ 1000x - x = 1.001001001... - 0.001001001...
⇒ 999x = 1
⇒ x = 1/999
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