Chapter 1, Problem 1RE

To determine

Classify the given numbers as one or more of the following: natural number, integer, rational number or real number.

Answer to Problem 1RE

Solution: Natural number: $\underset{\_}{\sqrt{16}}$

Integer: $-2,0,\sqrt{16}$

Rational Number: $-2,0,\frac{1}{2},1.23,\sqrt{16}$

Real Number: $-2,\frac{1}{2},0,1.23,\sqrt{7,}\sqrt{16}$

Explanation of Solution

Explanation:Given: The given numbers are $-2,\frac{1}{2},0,1.23,\sqrt{7,}\sqrt{16}$ .

Calculation:Natural number: These numbers start from 1 and we use these numbers for counting things. The set of all natural numbers is $\{1,2,3,\mathrm{.....}\}$ .

From the given numbers only $\sqrt{16}$ can be represented as a natural number. We know that $\sqrt{16}=4$ . Since 4 is a natural number, therefore, $\sqrt{16}$ is also a natural number.

Integer: Integers are whole numbers that means not written as a fraction. They can be positive or negative or zero. The set of integers can be written as $\{\mathrm{...},-3,-2,-1,0,1,2,3,\mathrm{...}\}$ .

So, in this category we have: $-2,0,\sqrt{16}$ .

Rational Number: These are the numbers which can be written in the form of $\frac{a}{b},b\ne 0$ , where “a” and “b” are integers.

So, in this category we have: $-2,0,\frac{1}{2},1.23,\sqrt{16}$

Real Number: Any number which can be represented on the number line is Real number it could be positive, negative or fraction.

So, in this category we have: $-2,\frac{1}{2},0,1.23,\sqrt{7,}\sqrt{16}$

Conclusion:$-2$ is aninteger, a real number and a rational number.

  $\frac{1}{2}$ is a rational number and a real number.

  $0$ is aninteger, a real number and a rational number.

  $1.23$ is a rational number and a real number.

  $\sqrt{7}$ is a real number.

  $\sqrt{16}$ is an integer, anatural number, a rational number and a real number.