Chapter P, Problem 1RE

a.

To determine

To find:

Natural numbers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{4\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Natural Numbers are the counting numbers that are used for counting and are greater than 0 i.e. 1,2,3,…

From the given set of numbers, it is seen that 4 is the only counting number.

Therefore natural numbers in the given set is $\left\{4\right\}$.

b.

To determine

To find:

Whole Numbers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{0,4\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Whole Numbers are natural numbers and 0 together i.e counting numbers that are used for counting and are greater than or equal to 0 i.e. 0,1,2,3,…

From the given set of numbers, it is seen that 0,4 are the counting numbers greater than or equal to 0.

Therefore whole numbers in the given set are $\left\{0,4\right\}$.

c.

To determine

To find:

Integers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{-5,0,4\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Integers are those numbers that can be written without a fractional component. They include 0, all natural numbers and the negatives of the natural numbers i.e. …-3,-2,-1,0,1,2,3,…

From the given set of numbers, it is seen that -5,0,4 come under the category of integers.

Therefore integers in the given set is $\left\{-5,0,4\right\}$.

d.

To determine

To find:

Rational Numbers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{-5,0,0.2,0.\overline{31},\frac{1}{2},4\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Rational Numbers are those numbers that can be written as a fraction $\frac{p}{q}$ where q is not equal to 0. They include all the recurring decimals, fractions, 0, all natural numbers and the negatives of the natural numbers. In simpler terms, all the real numbers that are not irrational are rational numbers.

From the given set of numbers, it is seen that $-5,0,0.2,0.\overline{31},\frac{1}{2},4$ come under the category of rational numbers.

Therefore rational numbers in the given set is $\left\{-5,0,0.2,0.\overline{31},\frac{1}{2},4\right\}$.

e.

To determine

To find:

Irrational Numbers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{\sqrt{7},\sqrt{12}\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Irrational Numbers are those numbers that cannot be written as rational numbers. They include all the non-recurring decimal numbers i.e. the decimal part of the number does not occur again in the same pattern. For example $\sqrt{2}=\mathrm{1.414213....}$ This is a never ending decimal. All the numbers that do not have a root come under this category

From the given set of numbers, it is seen that $\sqrt{7},\sqrt{12}$ come under the category of irrational numbers.

Therefore irrational numbers in the given set is $\left\{\sqrt{7},\sqrt{12}\right\}$.

f.

To determine

To find:

Real Numbers from the set $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$ .

Answer to Problem 1RE

$\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$.

Explanation of Solution

Given information:

Set of numbers is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$

Calculation:

Real numbers is the set of all rational and irrational numbers together. All numbers that are not complex come under real numbers.

Since there are no complex numbers in the given set, all are real numbers

Therefore real numbers in the given set is $\left\{4,\sqrt{7},-5,\frac{1}{2},0.\overline{31},0,0.2,\sqrt{12}\right\}$.