Question

With what smallest number should 0.xyxyxyxy ........ be multiplied to get an integral value. (x and y are distinct non-negative integers
a)999
b)100
c)99
d)45

Answer 1

Answer: The correct answer to this question is option (c) 99

Step-by-step explanation:

In question it is stated that x and y are distinct and non negative integers.

Which means, x and y are separate positive integers.

Let A = 0.xyxyxyxyxy...                       ...............................   equation 1

Multiplying both the sides by 100, we get

100A = xy.xyxyxyxyxyxy...                   ................................ equation 2

Now, Subtracting equation 1 from 2 , we have

100A - A = xy.xyxyxyxy... - 0.xyxyxyxy...

99A = xy

∴A = $\frac{xy}{99}$

∴ 99 is the smallest number should 0.xyxyxyxy ........ be multiplied to get an integral value.

Answer 2

Topic - Rationalising

• Rational number: The numbers of the form x/y with both x, y as integers and non-zero y are called rational numbers.
• Examples: 1/1, 1/7, 0/2, 27/560, etc.

Let, A = 0.xyxyxyxy......

Multiplying 100 in both sides, we get

100A = xy.xyxyxyxy...

∴ 100A - A = xy.xyxyxyxy... - 0.xyxyxyxy...

or, 99A = xy

or, A = xy/99

or, 0.xyxyxyxy... = xy/99

Hence we conclude that 99 is the smallest number, multiplied by which we get an integral value.

Option (C) = 99 is correct.