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Question

Which of the following rational numbers lie between 254 and 223?


  1. Integers

  2. Whole number

  3. Irrational number

  4. Non integers


Solution

The correct option is B

Whole number


Rational numbers can be compared by making their denominators equal.
We have the following fractions - 223,254,152,172,132 and the integer 8 which can be written as 81
LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions is 12.
Converting all the fractions above into fractions with a common denominator, we get:
223=22×43×4=8812
254=25×34×3=7512
132=13×62×6=7812
152=15×62×6=9012
172=17×62×6=10212
8=81=8×121×12=9612

Arranging these fractions in an ascending order, we get
7512,7812,8812,9012,9612,10212

Thus, the number between 223 and 254 is 7812, i.e. 132

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