Chapter 2.CM, Problem 1CM

To determine

To check:

The sets that the identified numbers belong to which number.

Answer to Problem 1CM

Solution:

Identified numbers	Natural numbers	Whole numbers	Integers	Irrational numbers	Real numbers
$9$	$X$	$X$	$X$		$X$
$-\frac{1}{2}$			$X$		$X$
$-\sqrt{7}$				$X$	$X$
$0.\overline{3}$			$X$		$X$
$\frac{8}{3}$			$X$		$X$
$-2$		$X$	$X$		$X$
$0$	$X$	$X$	$X$		$X$

Explanation of Solution

Natural numbers:

A natural number is a counting number of the set $\left\{1,2,3,\mathrm{4....}\right\}$.

The set of natural number is N.

Whole numbers:

Whole numbers are positive numbers, including zero, without any decimal or fractional parts.

The set of whole numbers is represented by $\left\{0,1,2,3,\mathrm{4....}\right\}$

Integers:

An integer is whole number that can be positive, negative or zero.

Example:

$-5,1,0,8$

Rational numbers:

A rational numbers is a number than can expressed as a fraction of $\frac{a}{b}$, where a and b are integer, $b\ne 0$

Example:

$16,-8,\frac{1}{2},\mathrm{1.333...},3.35,-\frac{3}{4}$

Irrational numbers:

An irrational number cannot be expressed in the form $\frac{a}{b}$$\frac{a}{b}$, where a and b are integer, $b\ne 0$

Example:

$\pi ,\sqrt{3},\sqrt{\frac{3}{2}}$

Real numbers:

A real numbers are all of the numbers represented on the number line.

It includes natural, whole, integers, rational and irrational numbers.

Example:

$\frac{5}{3},0.01\overline{2},\sqrt{3},5,1,\mathrm{..}$

Calculation:

From, the above definitions, we check mark the table

Identified numbers	Natural numbers	Whole numbers	Integers	Irrational numbers	Real numbers
$9$	$X$	$X$	$X$		$X$
$-\frac{1}{2}$			$X$		$X$
$-\sqrt{7}$				$X$	$X$
$0.\overline{3}$			$X$		$X$
$\frac{8}{3}$			$X$		$X$
$-2$		$X$	$X$		$X$
$0$	$X$	$X$	$X$		$X$

Final statement:

Hence, the check marked the numbers in the table.