Chapter 1.3, Problem 2LC

To determine

To find: the name of subsets of the real numbers to which the number belongs.

Answer to Problem 2LC

  $-7$ belongs to set of rational numbers, integers.

Explanation of Solution

Given:

  $-7$ .

Concept used:

Number system or real number $\left(R\right)$

consist of two types namely:

Rational numbers and irrational numbers.

Rational numbers: all terminating or recurring decimals.

irrational numbers: all non -terminating and non- recurring decimals.

Rational numbers $\left(Q\right)$ is divided by two types:

Integers and non-integers.

Integers are those numbers which are in the form composite number without the fraction and non-integers are numbers in fractions.

Integers are further divided into two types as:

Negative numbers and whole numbers and whole number is further divided into two type as natural number and zero.

From the above description it is clear that the rational and irrational numbers together form the set of real numbers.

Calculation:

Consider the number:

  $-7$ .

Write the subset or subsets of the real numbers for which the number contains.

The numbers of the form $\frac{a}{b}$ , where $a\text{ and }b$ are integers and $b\ne 0$ are called rational numbers.

Mathematically,

  $Q=\left\{\frac{a}{b};a\in z,b\in z,b\ne 0\right\}$ is the set of rational numbers.

All naturals numbers together with $0$ and the negatives of all counting numbers form the set of integers denoted by $Z$ .

Thus, $-7$ is a rational number and an integer.

Hence, $-7$ belongs to set of rational numbers, integers.