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Mathematics

Case Study

Ms Mehta teaches maths in a school. One day after teaching the lesson of number system, she wanted to check the understanding of the students of her class. So, she wrote two numbers, 311 and 0.52‾\dfrac{3}{11}\text{ and } 0.\overline{52} on the blackboard and asked few questions based on them. You please try to answer the following questions asked by Ms Mehta.

  1. The decimal expansion of 311\dfrac{3}{11} is:
    (a) terminating
    (b) non-terminating
    (c) non-terminating non-repeating
    (d) non-terminating repeating

  2. 0.52‾0.\overline{52} is:
    (a) non-terminating non-repeating
    (b) non-terminating repeating
    (c) non-terminating
    (d) terminating

  3. The decimal form of 311\dfrac{3}{11}:
    (a) 0.27
    (b) 0.2727
    (c) 0.27‾0.\overline{27}
    (d) 0.3

  4. 0.52‾0.\overline{52} as vulgar fraction becomes:

    (a) 5299\dfrac{52}{99}

    (b) 52100\dfrac{52}{100}

    (c) 2625\dfrac{26}{25}

    (d) 1325\dfrac{13}{25}

  5. The sum of 0.52‾ and 3110.\overline{52} \text{ and } \dfrac{3}{11} is :
    (a) 7999\dfrac{79}{99}

    (b) 7099\dfrac{70}{99}

    (c) 5299\dfrac{52}{99}

    (d) 4099\dfrac{40}{99}

Rational Irrational Nos

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Answer

1. On dividing,

311=0.27‾\dfrac{3}{11} = 0.\overline{27}

Hence, Option (d) is the correct option.

2. 0.52‾0.\overline{52} = 0.525252…

Hence, Option (b) is the correct option.

3. 311\dfrac{3}{11} = 0.272727…. = 0.27‾0.\overline{27}

Hence, Option (c) is the correct option.

4. Given,

Let x = 0.525252..     ………(1)

Multiply both side by 100(as two digits are recurring)

⇒ 100x = 52.5252..     ………(2)

Subtracting eqn (1) from eqn (2), we get :

⇒ 100x - x = 52.5252.. - 0.525252

⇒ 99x = 52

⇒ x = 5299\dfrac{52}{99}.

Hence, Option (a) is the correct option.

5. From part 4,

0.52‾=52990.\overline{52} = \dfrac{52}{99}

Adding 5299\dfrac{52}{99} and 311\dfrac{3}{11}

⇒5299+311⇒52+2799⇒7999.\Rightarrow \dfrac{52}{99} + \dfrac{3}{11} \\[1em] \Rightarrow \dfrac{52 + 27}{99} \\[1em] \Rightarrow \dfrac{79}{99}.

Hence, Option (a) is the correct option.

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