NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 1

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Q-1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non- terminating repeating decimal expansion:

  1. 133125

  2. 178

  3. 64455

  4. 151600

  5. 29343

  6. 232352

  7. 129225775

  8. 615

  9. 3550

  10. 77210

Solution:

  • We know that if the denominator of a rational number has no prime factors other than 2 or 5

  • Then it is expressible as a terminating, otherwise it has non- terminating repeating decimal representation

  • Thus, we will have to check the prime factors of the denominators of each of the given rational numbers

    Given the terminating decimal in a fraction it represent the finite number of digits

    Given the Terminnating Decimal

    Given the terminating decimal in a fraction it represent the finite number of digits

    Given the non-terminating decimal whichrepresent an infinite number

    Given the Non Terminating Decimal

    Given the non-terminating decimal whichrepresent an infinite number

  1. 133125

    pq Is terminating if

    • p and q are co-prime

    • And q is of the form 2n5m Where n and m are non-negative integers

    Checking Co-prime

    13 and 3125 have no common factors,

    So, 13 and 3125 are co-prime

    For denominator 3125

    Given the factor value anf find the fraction of 3125

    Given the Factors of 3125

    Given the factor value anf find the fraction of 3125

    Hence 3125=5×5×5×5×5

    =55

    Denominator=55

    =1×55

    =20×55

    So, denominator is of the form 2n5m

    Where n=0,m=5

    Thus 133125 is terminating decimal

  2. 178

    pq Is terminating if

  • p and q are co-prime

  • And q is of the form 2n5m Where n and m are non-negative integers

Checking Co-prime

17 and 8 have no common factors,

So, 17 and 8 are co-prime

For denominator 8

Given the factors and find the factor of 8

Given the Factors of 8

Given the factors and find the factor of 8

Hence 8=2×2×2

=23

Denominator=23

=1×23

=50×23

So, denominator is of the form 2n5m

Where n=3,m=0

Thus 178 is terminating decimal

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