NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 3

In the questions below, find the types of decimals.

Q VI) 232352

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

23 and 2352 have no common factors, so, 23 and 2352 are co-prime

For denominator 2352

Denominator=23×52

So, denominator is of the form 2n5m

Where n=3,m=2

Thus 232352 is terminating decimal

Q VII) 129225775

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

129 and 225775 have no common factors,

So, 129 and 225775 are co-prime

For denominator 225775

Denominator=225775

So, denominator is not of the form 2n5m

Thus 129225775 has a non-terminating repeating decimal

Q VIII) 615

615=25

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

2 and 5 have no common factors,

So, 2 and 5 are co-prime

For denominator 5

Denominator=5

=51

=1×51

=20×51

So, denominator is of the form 2n5m

Where n=0,m=1

Thus 25 i.e. 615 is a terminating decimal

Q IX) 3550

3550=710

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

7 and 10 have no common factors,

So, 7 and 10 are co-prime

For denominator 10

Denominator=10

=2×5

=21×51

So, denominator is of the form 2n5m

Where n=1,m=1

Thus 710 i.e. 3550 is a terminating decimal

Q X) 77210

77210=1130

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

11 and 30 have no common factors, so, 11 and 30 are co-prime

For denominator 30

Denominator=30

=2×3×5

=21×51

So, denominator is not of the form 2n5m

Thus 1130 i.e. 77210 is a non-terminating repeating decimal

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