Question

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venn diagrams and real numbers
combining the set of rational numbers and the set of irrational numbers produces the set of real numbers. you can use a venn diagram to represent how the sets within the set of real numbers are related.

1. the venn diagram shows the relationship among the six sets of numbers. write each of the numbers in the appropriate section of the venn diagram.

$-101$ $-6.41$ $0$ $|2|$ $sqrt{0.25}$ $\frac{sqrt{9}}{16}$ $pi$ $6\frac{1}{4}$
$-sqrt{9}$ $-sqrt{2}$ $1.0205 \times 10^{-23}$ $0.\overline{91}$ $sqrt{2}$ $\frac{100}{11}$ $sqrt{100}$
$-1$ $0.001$ $0.5\\%$ $1.523232323...$ $4^2$ $627,513$
$-\frac{3}{8}$ $-0.3$ $0.25$ $212\\%$ $|-3|$ $3.21 \times 10^{12}$
real numbers
rational numbers
irrational numbers
integers
whole numbers
natural numbers

Explanation:

Step1: Classify Natural Numbers

Natural numbers are positive counting numbers (1,2,3,...).
Identify values that fit:
$4^2=16$, $|2|=2$, $|-3|=3$, $\sqrt{100}=10$, $627,513$, $3.21\times10^{12}$

Step2: Classify Whole Numbers

Whole numbers include natural numbers + 0.
Add to natural numbers: $0$

Step3: Classify Integers

Integers include whole numbers + negative whole numbers.
Add to whole numbers: $-101$, $-1$, $-\sqrt{9}=-3$

Step4: Classify Non-Integer Rationals

Rationals are numbers that can be written as $\frac{a}{b}$ ($a,b$ integers, $b
eq0$); include non-integer values here.
Identify values: $-6.41$, $6\frac{1}{4}=\frac{25}{4}$, $1.0205\times10^{-23}$, $0.\overline{91}$, $\frac{100}{11}$, $0.001$, $0.5\%=\frac{0.5}{100}=\frac{1}{200}$, $1.523232323...$, $212\%=\frac{212}{100}$, $-\frac{3}{8}$, $-0.3=-\frac{3}{10}$, $0.25=\frac{1}{4}$, $\sqrt{0.25}=0.5=\frac{1}{2}$, $\frac{\sqrt{9}}{16}=\frac{3}{16}$

Step5: Classify Irrational Numbers

Irrational numbers cannot be written as $\frac{a}{b}$; non-repeating, non-terminating decimals.
Identify values: $\pi$, $-\sqrt{2}$, $\sqrt{2}$

Answer:

Natural Numbers:

$|2|$, $\sqrt{100}$, $4^2$, $|-3|$, $627,513$, $3.21\times10^{12}$

Whole Numbers:

$0$, $|2|$, $\sqrt{100}$, $4^2$, $|-3|$, $627,513$, $3.21\times10^{12}$

Integers:

$-101$, $-1$, $-\sqrt{9}$, $0$, $|2|$, $\sqrt{100}$, $4^2$, $|-3|$, $627,513$, $3.21\times10^{12}$

Rational Numbers (Non-Integer):

$-6.41$, $6\frac{1}{4}$, $1.0205\times10^{-23}$, $0.\overline{91}$, $\frac{100}{11}$, $0.001$, $0.5\%$, $1.523232323...$, $212\%$, $-\frac{3}{8}$, $-0.3$, $0.25$, $\sqrt{0.25}$, $\frac{\sqrt{9}}{16}$

Irrational Numbers:

$\pi$, $-\sqrt{2}$, $\sqrt{2}$

Real Numbers:

All listed numbers (the union of rational and irrational numbers above)