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 :

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. This number is terminating.

  2. This number is recurring non-terminating.

  3. This number is terminating.

  4. This number is recurring non-terminating.

  5. This number is recurring non-terminating.

  6. This number is terminating.

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

Solution:

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

Solution:

Image of recurring decimal

Recurring Decimal

Image of recurring decimal

  1. To be written in form.

    One digit 6 is repeating

    We multiply it with 10 on both sides.

  2. To be written in form.

    One digit 7 is repeating

    We multiply it with 10 on both sides.

  3. To be written in form.

    Here three digits repeats, we multiply with 1000