Answer
a. Natural: $\sqrt{100}$
b. Whole: $0,\sqrt{100}$
c. Integer: $-9,0,\sqrt{100}$
d. Rational: $-9,-\displaystyle \frac{4}{5},0.25,9.2,\sqrt{100}$
e. Irrational: $\sqrt{3}$
f. Real: all of them
Work Step by Step
The set of natural numbers is { 1, 2, 3, 4, 5, ... } .
The set of whole numbers is { 0, 1, 2, 3, 4, 5, ... }
The set of integers is {... , -4, -3, -2, -1,0, 1, 2, 3, 4,...}
The set of rational numbers$: \displaystyle \frac{a}{b},\ b\neq 0$, and b integers
Irrational numbers: are not rational (can not be written as $\displaystyle \frac{a}{b},\ b\neq 0$)
Real numbers: all rational and irrational numbers.
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$-9$ is a negative integer, can be written as $\displaystyle \frac{-9}{1}$ so is also rational
$-\displaystyle \frac{4}{5}$ is a rational number
$0$ is a whole number, an integer, rational ($\dfrac 01$)
$0.25=\displaystyle \frac{25}{100}$ is a rational number
$\sqrt{3 }$ is irrational
$9.2=\displaystyle \frac{92}{10}$ , rational
$\sqrt{100}=10,$ natural, whole, integer, rational.
a. Natural: $\sqrt{100}$
b. Whole: $0,\sqrt{100}$
c. Integer: $-9,0,\sqrt{100}$
d. Rational: $-9,-\displaystyle \frac{4}{5},0.25,9.2,\sqrt{100}$
e. Irrational: $\sqrt{3}$
f. Real: all of them
