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Standard IX
Mathematics
Decimal Expansion of Rational and Irrational Numbers
Question
The value of
1.999...
in the form
p
q
, where
p
and
q
are integers and
q
≠
0
, is:
1999
1000
2
1
9
19
10
A
1
9
B
19
10
C
2
D
1999
1000
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Solution
Verified by Toppr
Let
x
=
1.999...
Since, one digit is repeating, we multiply
x
by
10
, we get
10
x
=
19.99...
So,
10
x
=
18
+
1.999...
=
18
+
x
Therefore,
10
x
−
x
=
18
, i.e.,
9
x
=
18
i.e.,
x
=
18
9
=
2
1
=
2
Hence, option
D
is correct answer.
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Similar Questions
Q1
Question 9
The value of 1.999 ….. in the form of
p
q
, where p and q are integers and
q
≠
0
, is
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19
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B)
1999
1000
C)
2
D)
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, where p and q are integers and
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B)
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