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Byju's Answer

Standard VII

Mathematics

Integers

D is a real n...

Question

$D$ is a real number with non terminating digits $a_{1}$ and $a_{2}$ after the decimal point. Let $D = 0, a_{1} a_{2} a_{1} a_{2} . . . . . . . .$ with $a_{1} & a_{2}$ both not zero which of the following when multiplied by $D$ will necessarily give an integer ?

99

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18

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125

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75

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Solution

The correct option is A $99$
its straight question
give $D = 0. a b a b a b a b$ $(s a y - 1)$
Multiply both sides by $100$ $i . e .$
$100 D = a b . a b a b a b a b$ $(s a y - 2)$
now subtract $1$ from $2 .$ That gives
$99 D = a b => D = a b / 99$ hence it should be multiplied by $99 k$ to get an integer ab $.$

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D is a real number which noon terminating digits a1 and a2 after the decimal point. Let D= 0.a1 a2 a1 a2........with a1 and a2 both not zero which of the following when mutiplied by D will necessarily give an integer?

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D is a real number with non terminating digits a1 and a2 after the decimal point. Let D=0,a1a2a1a2........ with a1&a2 both not zero which of the following when multiplied by D will necessarily give an integer ?

The correct option is A 99its straight questiongive D=0.abababab (say−1) Multiply both sides by 100 i.e. 100D=ab.abababab (say−2)now subtract 1 from 2. That gives99D=ab=>D=ab/99 hence it should be multiplied by 99k to get an integer ab.

$D$ is a real number with non terminating digits $a_{1}$ and $a_{2}$ after the decimal point. Let $D = 0, a_{1} a_{2} a_{1} a_{2} . . . . . . . .$ with $a_{1} & a_{2}$ both not zero which of the following when multiplied by $D$ will necessarily give an integer ?