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. 36100

  2. 111

  3. 418

  4. 313

  5. 211

  6. 329400

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. 36100=0.36 This number is terminating.

  2. 111=0.09¯ This number is recurring non-terminating.

  3. 418=338=4.125 This number is terminating.

  4. 313=0.230769¯ This number is recurring non-terminating.

  5. 211=0.18¯ This number is recurring non-terminating.

  6. 329400=0.8225 This number is terminating.

Q.2 You know that 17=0.142857¯ . Can you predict what the decimal expansions of 27,37,47,57,67 are, without actually doing the long division? If so, How.

Solution:

27=2×17=0.285714¯

37=3×17=0.428571¯

47=4×17=0.571428¯

57=5×17=0.714285¯

67=6×17=0.857142¯

Q.3 Express the following in the form of pq , where p and q are integers and q0 .

  1. 0.6¯

  2. 0.47¯

  3. 0.001¯

Solution:

Image of recurring decimal

Recurring Decimal

Image of recurring decimal

  1. x=0.6¯=0.666 To be written in pq form.

    One digit 6 is repeating

    We multiply it with 10 on both sides.

    10x=6.6¯

    10x=6+x

    10xx=6

    9x=6

    x=69=23

  2. x=0.47¯=0.47777 To be written in pq form.

    One digit 7 is repeating

    We multiply it with 10 on both sides.

    10x=4.7¯

    10x=4.3+0.47¯

    10x=4.3+x

    10xx=4.3

    9x=4.3

    x=4.39=4390

  3. x=0.001¯=0.001 To be written in pq form.

    Here three digits repeats, we multiply with 1000

    1000x=1.001¯

    1000x=1+x

    1000xx=1

    999x=1

    x=1999

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