Answer :
To determine the type of number that \(\frac{3}{2}\) is, let's analyze step-by-step:
1. Rational Number:
- A rational number is defined as any number that can be expressed as the quotient or fraction \(\frac{p}{q}\) of two integers, where \(p\) and \(q\) are integers and \(q \neq 0\).
- In this case, \(\frac{3}{2}\) is expressed as a fraction \(\frac{3}{2}\), where 3 (the numerator) and 2 (the denominator) are both integers, and the denominator is not zero.
- Therefore, \(\frac{3}{2}\) is a rational number.
2. Natural Number:
- Natural numbers are the set of positive integers starting from 1 and increasing (1, 2, 3, 4, ...). Some definitions include zero, but they are always whole numbers.
- \(\frac{3}{2}\), when simplified or converted to a decimal, is 1.5.
- Since 1.5 is not a whole number and does not belong to the set of natural numbers, \(\frac{3}{2}\) is not a natural number.
Summarizing, \(\frac{3}{2}\) is a rational number but not a natural number.
Therefore, the answers are:
(i) Rational - True
(ii) Natural - False
1. Rational Number:
- A rational number is defined as any number that can be expressed as the quotient or fraction \(\frac{p}{q}\) of two integers, where \(p\) and \(q\) are integers and \(q \neq 0\).
- In this case, \(\frac{3}{2}\) is expressed as a fraction \(\frac{3}{2}\), where 3 (the numerator) and 2 (the denominator) are both integers, and the denominator is not zero.
- Therefore, \(\frac{3}{2}\) is a rational number.
2. Natural Number:
- Natural numbers are the set of positive integers starting from 1 and increasing (1, 2, 3, 4, ...). Some definitions include zero, but they are always whole numbers.
- \(\frac{3}{2}\), when simplified or converted to a decimal, is 1.5.
- Since 1.5 is not a whole number and does not belong to the set of natural numbers, \(\frac{3}{2}\) is not a natural number.
Summarizing, \(\frac{3}{2}\) is a rational number but not a natural number.
Therefore, the answers are:
(i) Rational - True
(ii) Natural - False
