Chapter A.11, Problem 1AYU

To determine

The rational numbers and integers in the set $\left\{-3,0,\sqrt{2},\frac{6}{5},\pi \right\}$.

Answer to Problem 1AYU

Solution:

The solution is $\left\{-3,0\right\}$ are the integers and $\left\{-3,0,\frac{6}{5}\right\}$ are the rational numbers in the given set.

Explanation of Solution

Given Information:

The given rational number $\left\{-3,0,\sqrt{2},\frac{6}{5},\pi \right\}$.

Explanation:

Integers are the set of numbers $\left\{\mathrm{..............}-3,-2,-1,0,1,2,\mathrm{3..............}\right\}$.

They consist of all the positive and negative numbers including 0.

Thus,

$\left\{-3,0\right\}$ Are the integers in the given set?

Rational numbers are numbers in sets.

$\left\{x|x=\frac{a}{b},\text{where }a,b\text{are ntegers and }b\ne 0\right\}$.

Every rational number may be represented by a decimal that either terminates or is non-terminating with a repeating block of digits.

Thus, the rational numbers in the given set are $\left\{-3,0,\frac{6}{5}\right\}$.

Hence, $\left\{-3,0\right\}$ are the integers and $\left\{-3,0,\frac{6}{5}\right\}$ are the rational numbers in the given set.