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

In the questions below, find the types of decimals.

Q VI) Equation

Equation Is terminating if

  • p and q are co-prime

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

Checking Co-prime

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

For denominator Equation

Equation

So, denominator is of the form Equation

Where Equation

Thus Equation is terminating decimal

Q VII) Equation

Equation Is terminating if

  • p and q are co-prime

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

Checking Co-prime

129 and Equation have no common factors,

So, 129 and Equation are co-prime

For denominator Equation

Equation

So, denominator is not of the form Equation

Thus Equation has a non-terminating repeating decimal

Q VIII) Equation

Equation

Equation Is terminating if

  • p and q are co-prime

  • And q is of the form Equation 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

Equation

Equation

Equation

Equation

So, denominator is of the form Equation

Where Equation

Thus Equation i.e. Equation is a terminating decimal

Q IX) Equation

Equation

Equation Is terminating if

  • p and q are co-prime

  • And q is of the form Equation 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

Equation

Equation

Equation

So, denominator is of the form Equation

Where Equation

Thus Equation i.e. Equation is a terminating decimal

Q X) Equation

Equation

Equation Is terminating if

  • p and q are co-prime

  • And q is of the form Equation 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

Equation

Equation

Equation

So, denominator is not of the form Equation

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

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