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

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In the questions below, find the types of decimals.

Q VI)

Is terminating if

  • p and q are co-prime

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

Checking Co-prime

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

For denominator

So, denominator is of the form

Where

Thus is terminating decimal

Q VII)

Is terminating if

  • p and q are co-prime

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

Checking Co-prime

129 and have no common factors,

So, 129 and are co-prime

For denominator

So, denominator is not of the form

Thus has a non-terminating repeating decimal

Q VIII)

Is terminating if

  • p and q are co-prime

  • And q is of the form 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

So, denominator is of the form

Where

Thus i.e. is a terminating decimal

Q IX)

Is terminating if

  • p and q are co-prime

  • And q is of the form 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

So, denominator is of the form

Where

Thus i.e. is a terminating decimal

Q X)

Is terminating if

  • p and q are co-prime

  • And q is of the form 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

So, denominator is not of the form

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