Question

Which of the following numbers are:

$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$

1. natural numbers?
2. whole numbers?
3. integers?
4. rational numbers

Answer 1

(I) Finding natural numbers from $\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$:

The counting numbers $1,2,3,4,...$ are called natural numbers.

Therefore , the natural numbers from$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$ are $\left\{2,7\right\}$

(II) Finding whole numbers from $\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$:

When zero is included in set of natural numbers then those numbers are called whole number.

Therefore, the whole numbers from$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$ are $\left\{0,2,7\right\}$

(III) Finding integers from $\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$:

The whole number together with the negative numbers are called integers.

Therefore, the integers from$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$ are $\left\{-8,0,2,7\right\}$

(IV) Finding rational numbers from $\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$:

The set of numbers in form of $\frac{p}{q}$ which includes zero, positive and negative fractions are called rational number, where,$q\ne 0$

Therefore, the rational numbers from$\left\{7,\frac{3}{2},-\frac{9}{5},-8,0,2,\frac{1}{4}\right\}$ are $\left\{-8,-\frac{9}{5},0,\frac{1}{4},\frac{3}{2},2,7\right\}$