NCERT Class 9 Solutions: Number Systems (Chapter 1) Exercise 1.3 – Part 1

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Q.1 Write the following in decimal form and say what kind of decimal expansion each has :

  1. Equation

  2. Equation

  3. Equation

  4. Equation

  5. Equation

  6. Equation

Solution:

  • A decimal expansion 2 types:

    1st is terminating decimal means A decimal number that has digits that do not go on forever.

    2nd is Recurring non terminating decimal means A decimal number that has digits that go on forever.

    Terminating vs non terminating expansions and their sub-types

    Types of Decimal Expansions

    Terminating vs non terminating expansions and their sub-types

  1. Equation This number is terminating.

  2. Equation This number is recurring non-terminating.

  3. Equation This number is terminating.

  4. Equation This number is recurring non-terminating.

  5. Equation This number is recurring non-terminating.

  6. Equation This number is terminating.

Q.2 You know that Equation . Can you predict what the decimal expansions of Equation are, without actually doing the long division? If so, How.

Solution:

Equation

Equation

Equation

Equation

Equation

Q.3 Express the following in the form of Equation , where p and q are integers and Equation .

  1. Equation

  2. Equation

  3. Equation

Solution:

Image of recurring decimal

Recurring Decimal

Image of recurring decimal

  1. Equation To be written in Equation form.

    One digit 6 is repeating

    We multiply it with 10 on both sides.

    Equation

    Equation

    Equation

    Equation

    Equation

  2. Equation To be written in Equation form.

    One digit 7 is repeating

    We multiply it with 10 on both sides.

    Equation

    Equation

    Equation

    Equation

    Equation

    Equation

  3. Equation To be written in Equation form.

    Here three digits repeats, we multiply with 1000

    Equation

    Equation

    Equation

    Equation

    Equation

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