Number Systems

1, 44, 170, 5000

-36, -2, 0, 5, 79

$\frac{1}{5},5.7,\frac{10}{5},6.8$

The most well known example of an irrational number is pi ($\mathrm{\pi }$), this is a number that has a decimal that goes on forever without repeating any pattern;

$4+3\mathit{i},12+6\mathit{i},7+\frac{1}{2}\mathit{i}$

Which number system or systems does $\sqrt{46}$ belong to?

Solution:

To identify this you are able to use your calculator to solve the square root to see what type of number it is;

$\sqrt{46}=6.7823...$

Since the decimal does not terminate or repeat, this is an irrational number.

To which number system or systems does $\sqrt{64}$ belong to?

Solution:

Once again you can solve the square root to identify the type of number;

$\sqrt{64}=8$

Since $\sqrt{64}$ is equal to 8, $\sqrt{64}$ belongs to the number systems of, natural numbers, whole numbers, integers and rational numbers.

Graph the set of numbers $x\ge 1$

Solution:

To do this you need to first start by drawing a number line, the first number that is included is 1. To show that x could equal one you draw a filled dot above the number. Since there is no end to the graph, rather than drawing all of the numbers onto the graph you can simply draw an arrow going past the last number to indicate it is continuing;

Graphing real numbers example, Thomas-Gay - StudySmarter Originals

Graph the set of numbers id="2600988" role="math" $x<10$

Solution:

For this example you need to first start by drawing your number line, then you can begin to input the information. Since this time x is smaller than 10 but does not include 10, the circle above 10 will not be colored in.

Graph the set of numbers $x\le \frac{4}{5}$

Solution:

For this example you need to first start by drawing your number line, then you can begin to input the information. Since the x is smaller than and includes $\frac{4}{5}$, the circle above $\frac{4}{5}$ will be colored in.

Graph the set of numbers $x\ge -6$

Solution:

To begin with, draw out your number line, then you can start to input the information. Since x is bigger then or equal to -6, the circle above the -6 should be colored in.