Question

Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest.

The square root of 105, -4, 4/3

Answer 1

`√(105)` has no fraction that can represent it, therefore is an irrational number.

-4 is not a decimal, but is negative. It is an integer.

4/3 is a fraction, so it is a rational number.

Answer 2

√105 is belongs to irrational number.

-4 is belongs to integers as well as rational number.

4/3 is belongs to rational number.

Explanation:

Consider the provided numbers.

Integers: Integers are the set of whole number and the negatives of the natural numbers, i.e, … ,-2, -1, 0, 1, 2, …

Rational number: A number is said to be rational, if it is in the form of p/q. Where p and q are integer and denominator is not equal to 0.The decimal expansion of rational numbers may terminate or become periodic.

Irrational number: A number is irrational if it cannot be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.

Consider the number √105 = 10.2469...

Since, the decimal expansion is neither terminate nor periodic so √105 is an irrational number.

Consider the number -4.

The number -4 is an integers also it can be written in the form of p/q.

Thus, the number -4 is natural number and rational number.

Consider the number 4/3 = 1.333..

Here the decimal expansion is periodic thus the number 4/3 is rational number.