Explain each of the following in q/p form:
(i) 0.675(ii) 0.3 2 (iii) 0.12 3 (iv) 0.003 52 (v) 4.32 (vi) 2.317317317….
Answers
Answer:
1) 0.675
100x=67.5
1000x=675
X=675/1000
2) 0.32
100x=32
X=32/100
3) 0.123
1000x=123
X=123/1000
4) 0.00352
100000x=352
X=352/100000
5) 4.32
100x=432
X=432/100
Answer:
(i) 0.675 = 27/40
(ii) 0.32 = 8/25
(iii) 0.123 = 123/1000
(iv) 0.00352 = 11/3125
(v) 4.32 = 108/25
(vi) 2.317317317…. = 2315/999
Step-by-step explanation:
Proper fractions: If two numbers are written in the form of "q/p" then "q/p" is known as a proper fraction, where 'q' and 'p' are integers.
(i) 0.675
It can be written as:
675/1000 (removing the decimal and dividing by 1000)
The number in q/p form is 27/40, where q = 27 and p = 40.
(ii) 0.32
It can be written as:
32/100 (removing the decimal and dividing by 100)
The number in q/p form is 8/25, where q = 8 and p = 25.
(iii) 0.123
It can be written as:
123/1000 (removing the decimal and dividing by 1000)
The number in q/p form is 123/1000, where q = 123 and p = 1000.
(iv) 0.00352
It can be written as:
352/100000 (removing the decimal and dividing by 100000)
The number in q/p form is 11/3125, where q = 11 and p = 3125.
(v) 4.32
It can be written as:
432/100 (removing the decimal and dividing by 100)
The number in q/p form is 108/25, where q = 108 and p = 25.
(vi) 2.317317317...
Let x = 2.317317317....(1)
Now, 1000x = 2317.317317....(2)
Subtract equation (1) from (2)
1000x - x = 2317.317317 - 2.317317317
⇒ 999x = 2315
⇒ x = 2315/999
Therefore,the number in q/p form is 2315/999, where q = 2315 and p = 999.
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