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3. Express the following in the form, where p and q are integers and q +0.
(i) 0.6
(ii) 0.47
(iii) 0.001
Answers
Step-by-step explanation:
Non terminating repeating decimal has two types:
Pure Recurring decimals and mixed recurring decimals.
Pure recurring decimals:
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A decimal number in which all the digits after decimal point are repeated. E.g 0.675, 0.45
Mixed recurring decimals:
A decimal number in which at least 1 digits after the decimal point is not repeated and others are repeated. E.g , 0.72, 0. 645 e.t.c
Conversion of non terminating repeating decimal number:
i) put the given decimal number is equal to X.
ii) remove the bar if any and write a repeating digits at least twice..
iii) if the repeating decimal has one place repetition multiply by 10, if there is 2 place repetition multiply by 100 & so on.
iv) subtract the number in step ii from the number obtained step iii.
v) divide both sides of the equation by the coefficient of x.
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Solution:
(i) 0.6 = 0.666…
Let x = 0.666……. (1)
Here only one digit is repeating so multiply by 10 on both sides
10 × x = 10× 0.666….
10x = 6.666…. (2)
On subtracting equation 1 from equation 2
10x- x = 6.666…. - 0.666….
9x = 6
x = 9/ 6 = ⅔
Here , 0.6 = ⅔
(ii)
Let x= 0.47 = 0.4777…. (1)
Here, 1 digit is not repeating so multiply eq. 1 by 10
10 × x = 10 × 0.47777
10 x = 4.7777…… (2)
Now only 1 digit is repeating so multiply eq 2 by 10 we get
10 × 10x = 10 × 4.777….
100 x = 47.777….. (3)
On subtracting equation 2 from equation 3 we get
100 x-10 x= 47.777…. - 4.777….
90 x=43
X=43/90
Here, 0.47 = 43/90
(iii) 0.001 = 0.001001001…
Let x = 0.001001001…. (1)
Here, 3 digit is repeating so multiply by 1000
1000 × x = 1000 × . 001001001….
1000x = 1.001001001…. (2)
On subtracting equation 1 from equation 2
1000x -x = 1.001001001…. - 0.001001001...
999x = 1
x = 1/999
Hence ,0.001 = 1/999
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Hope this will help you...