Express each of the following decimal form into p/q
Answers
Answer:
0.5 = 5/10
Simplifying it in the same p/q form,
⇒ 0.5 = 1/2
It cannot be further simplified in p/q form.
1/2 is in the form p/q, where p = 1 and q = 2 are integers and q = 2 ≠ 0.
Hence, the answer is 1/2.
(ii).
This has to be converted in p/q form.
Let
,
That is, x = 3.88888… …(i)
Multiply 10 on both sides,
10 × x = 10 × 3.88888…
⇒ 10x = 38.8888… …(ii)
Subtracting equations (i) from (ii), we get
10x – x = 38.8888… - 3.88888…
⇒ 9x = 35
⇒ x = 35/9
35/9 is in the form of p/q, where p = 35 and q = 9 are integers and q = 9 ≠ 0.
Thus,
.
(iii).
This has to be converted in p/q form.
Let
,
That is, x = 0.363636… …(i)
Multiply 100 on both sides,
100 × x = 100 × 0.363636…
⇒ 100x = 36.363636… …(ii)
Subtracting equations (i) from (ii), we get
100x – x = 36.363636… - 0.363636…
⇒ 99x = 36
⇒ x = 99/36
Simplifying it further,
⇒ x = 11/4
11/4 is in the form of p/q, where p = 11 and q = 4 are integers and q = 4 ≠ 0.
Thus,
.
(iv).
This has to be converted in p/q form.
Let
,
That is, x = 3.127777… …(i)
Multiply 100 by equation (i),
100 × x = 100 × 3.127777…
⇒ 100x = 312.7777… …(ii)
Multiply 1000 by equation (ii),
1000 × x = 1000 × 3.127777…
⇒ 1000x = 3127.7777… …(iii)
Subtract equation (ii) from (iii), we get
1000x – 100x = 3127.7777… - 312.7777…
⇒ 900x = 2815
⇒ x = 2815/900
⇒ x = 563/180
563/180 is in the form of p/q, where p = 563 and q = 180 are integers and q = 180 ≠ 0.
Thus,
.
Answer:
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Step-by-step explanation:
a) 0.57
57/100
b) 0.176
176/1000
22/125
c) 25.125
25125/1000
201/8p'