Question

1. re - write each number in the venn diagram where it belongs.

-19 1.2 0 3
√10 √81 3.456 -4/11
-1.48298... π + 3 -44

1. list all classifications of the number.

a) √10
b) -44
c) 3
d) -4/11

1. check all boxes that apply to the number.

a) √81
b) 1.2
c) 0
d) 13
natural whole integer rational irrational real

Explanation:

Step1: Recall number - type definitions

Natural numbers are positive integers starting from 1 ($1, 2, 3,\cdots$), whole numbers are non - negative integers ($0, 1, 2,\cdots$), integers are whole numbers and their negatives ($\cdots,- 2,-1,0,1,2,\cdots$), rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$, irrational numbers cannot be written as a fraction, and real numbers are the union of rational and irrational numbers.

Step2: Classify numbers in part 1

• $-19$: Integer, Rational, Real.
• $1.2=\frac{6}{5}$: Rational, Real.
• $0$: Whole, Integer, Rational, Real.
• $3$: Natural, Whole, Integer, Rational, Real.
• $\sqrt{10}\approx3.162\cdots$: Irrational, Real.
• $\sqrt{81} = 9$: Natural, Whole, Integer, Rational, Real.
• $3.456=\frac{3456}{1000}$: Rational, Real.
• $-\frac{4}{11}$: Rational, Real.
• $-1.48298\cdots$ (non - repeating non - terminating): Irrational, Real.
• $\pi + 3\approx3.14159+3 = 6.14159\cdots$ (non - repeating non - terminating): Irrational, Real.
• $-44$: Integer, Rational, Real.

Step3: Classify numbers in part 2

a) $\sqrt{10}$: Irrational, Real.
b) $-44$: Integer, Rational, Real.
c) $3$: Natural, Whole, Integer, Rational, Real.
d) $-\frac{4}{11}$: Rational, Real.

Step4: Classify numbers in part 3

a) $\sqrt{81} = 9$: Natural, Whole, Integer, Rational, Real.
b) $1.2$: Rational, Real.
c) $0$: Whole, Integer, Rational, Real.
d) $13$: Natural, Whole, Integer, Rational, Real.

Answer:

1)

• $-19$: Integer, Rational, Real (in Rational circle and Integer subset).
• $1.2$: Rational, Real (in Rational circle).
• $0$: Whole, Integer, Rational, Real (in Whole subset, Integer subset, Rational circle).
• $3$: Natural, Whole, Integer, Rational, Real (in Natural subset, Whole subset, Integer subset, Rational circle).
• $\sqrt{10}$: Irrational, Real (in Irrational circle).
• $\sqrt{81}$: Natural, Whole, Integer, Rational, Real (in Natural subset, Whole subset, Integer subset, Rational circle).
• $3.456$: Rational, Real (in Rational circle).
• $-\frac{4}{11}$: Rational, Real (in Rational circle).
• $-1.48298\cdots$: Irrational, Real (in Irrational circle).
• $\pi + 3$: Irrational, Real (in Irrational circle).
• $-44$: Integer, Rational, Real (in Rational circle and Integer subset).

2)
a) Irrational, Real
b) Integer, Rational, Real
c) Natural, Whole, Integer, Rational, Real
d) Rational, Real
3)
a) Natural, Whole, Integer, Rational, Real
b) Rational, Real
c) Whole, Integer, Rational, Real
d) Natural, Whole, Integer, Rational, Real