Express 6.1977777..... in the form p/q, where p and q are integers and q is not equal to 0
Answers
Answered by
19
GIVEN THAT
X = 6.19777.....
_
X = 6.197 --------------(1)
SO, PERIODICITY = 1
10X = 61.9777..... ------(2)
FROM (1) & (2)
10X = 61.97777....
- X = 6.19777....
___________________
9X = 55.78
X = 55.78 / 9
X = 5578 /900
X = 2789 / 450
I.E P / Q = 2789 / 450
X = 6.19777.....
_
X = 6.197 --------------(1)
SO, PERIODICITY = 1
10X = 61.9777..... ------(2)
FROM (1) & (2)
10X = 61.97777....
- X = 6.19777....
___________________
9X = 55.78
X = 55.78 / 9
X = 5578 /900
X = 2789 / 450
I.E P / Q = 2789 / 450
sunayana1:
I have one doubt how can you take 10 or 100 or 1000
IT DEPENDS ON PERIDICITY
IF PERIODICITY IS 1 = 10X, 2=100X,3=1000X....
SO IT DEPEND ON PERIODICITY
Thanks a lot
wellcome
Answered by
9
GIVEN ⇒× = 6.19777.....
_
× = 6.197 --------------(1)
Multiply by 10 on both sides
10X = 61.9777..... ------(2)
Subtract 1 from 2
⇒10X - X = 61.97777....- 6.19777....
⇒9X = 55.78
⇒X = 55.78 / 9
⇒X = 5578 /900
⇒X = 2789 / 450
Thus,P/q= 2789 / 450
GIVEN ⇒× = 6.19777.....
_
× = 6.197 --------------(1)
Multiply by 10 on both sides
10X = 61.9777..... ------(2)
Subtract 1 from 2
⇒10X - X = 61.97777....- 6.19777....
⇒9X = 55.78
⇒X = 55.78 / 9
⇒X = 5578 /900
⇒X = 2789 / 450
Thus,P/q= 2789 / 450
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