# 2.13: Order of Real Numbers

**Basic**Created by: CK-12

**Practice**Order of Real Numbers

Suppose that you and three friends were playing a game where you each drew a number from a hat and the person with the highest number won. Let's say that you drew the number

### Ordering Real Numbers

#### Classifying Real Numbers

The chart above shows the relationships between different real numbers. If a number is in one category, it is also in all the categories connected above it.

#### Let's use the chart to categorize the following numbers:

- 0

Zero is a whole number, an integer, a rational number, and a real number.

- –1

–1 is an integer, a rational number, and a real number.

π3

36−−√9

#### Graphing and Ordering Real Numbers

Every real number can be positioned between two integers. Many times you will need to organize real numbers to determine the least value, greatest value, or both. This is usually done on a number line.

#### Let's plot the following rational numbers on a number line:

23

−37

5716

#### Now, let's compare π15 and 3√75−−√ :

First we simplify in order to better compare:

Now we rewrite

Since

so

Therefore,

### Examples

#### Example 1

Earlier, you were asked to determine which number out of

Notice that

Also, since

Using a calculator,

Thus the order of the numbers is

#### Example 2

For the numbers:

We need to simplify the numbers in order to classify them:

#### Example 3

For the numbers:

The four numbers are ordered as follows:

### Review

Classify the following numbers. Include all the categories that apply to the number.

0.25−−−−√ 1.35−−−−√ 20−−√ 25−−√ 100−−−√ - Place the following numbers in numerical order from lowest to highest.
6√261501.5−−−√1613 - Find the value of each marked point.

**Mixed Review**

- Simplify \begin{align*}\frac{9}{4}\div 6\end{align*}.
- The area of a triangle is given by the formula \begin{align*}A= \frac{b(h)}{2}\end{align*}, where \begin{align*}b=\end{align*} base of the triangle and \begin{align*}h =\end{align*} height of the triangle. Determine the area of a triangle with base \begin{align*}= 3\end{align*} feet and height \begin{align*}= 7\end{align*} feet.
- Reduce the fraction \begin{align*}\frac{144}{6}\end{align*}.
- Construct a table for the following situation: Tracey jumps 60 times per minute. Let the minutes be \begin{align*}\left \{0,1,2,3,4,5,6\right \}\end{align*}. What is the range of this function?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.13.

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### Image Attributions

Here you'll learn how to decide if a number is a whole number, an integer, a rational or irrational number, or a real number. You'll also learn how to put numbers in order and how to graph them on a number line.

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