Q.1.83 - Intermediate Algebra

Question

Given the numbers $-3, -\sqrt{2}, 0.\stackrel{-}{3} , \frac{9}{5}, 4,\sqrt{49}$ list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers. 

Step-by-Step Solution

Answer

a. Whole numbers : $4$

b. Integers : $-3,4,\sqrt{49}$

c. Rational numbers : $-3,0.\stackrel{-}{3,}\frac{9}{5},4,\sqrt{49}$

d. Irrational numbers : $-\sqrt{2}$

e. Real numbers : $-3, -\sqrt{2}, 0.\stackrel{-}{3} , \frac{9}{5}, 4,\sqrt{49}$

Given numbers

The numbers which are given are $-3, -\sqrt{2}, 0.\stackrel{-}{3} , \frac{9}{5}, 4,\sqrt{49}$

Required definitions

• The positive integers and zero are called whole numbers.
• The numbers with no decimals and fractions are called integers.
• The numbers which can be expressed in the $\frac{p}{q}$ format is rational number.
• The numbers which can not be expressed in the $\frac{p}{q}$format is irrational number.
• The numbers which are not imaginary are called real numbers.

Identifying the numbers

Following the mentioned definitions, we identify the given numbers and list them as,

a. whole numbers :$4$

b. Integers : $-3,4,\sqrt{49}$

c. Rational numbers :$-3,0.\stackrel{-}{3,}\frac{9}{5},4,\sqrt{49}$

d. Irrational numbers :$-\sqrt{2}$

e. Real numbers : $-3, -\sqrt{2}, 0.\stackrel{-}{3} , \frac{9}{5}, 4,\sqrt{49}$