<< Chapter < Page Chapter >> Page >
This figure consists of a Venn diagram. To start there is a large rectangle marked Real Numbers. The right half of the rectangle consists of Irrational Numbers. The left half consists of Rational Numbers. Within the Rational Numbers rectangle, there are Integers …, negative 2, negative 1, 0, 1, 2, …. Within the Integers rectangle, there are Whole Numbers 0, 1, 2, 3, … Within the Whole Numbers rectangle, there are Counting Numbers 1, 2, 3, …
This chart shows the number sets that make up the set of real numbers. Does the term “real numbers” seem strange to you? Are there any numbers that are not “real,” and, if so, what could they be?

Can we simplify −25 ? Is there a number whose square is −25 ?

( ) 2 = −25 ?

None of the numbers that we have dealt with so far has a square that is −25 . Why? Any positive number squared is positive. Any negative number squared is positive. So we say there is no real number equal to −25 .

The square root of a negative number is not a real number.

For each number given, identify whether it is a real number or not a real number: −169 64 .

  1. There is no real number whose square is −169 . Therefore, −169 is not a real number.
  2. Since the negative is in front of the radical, 64 is −8 , Since −8 is a real number, 64 is a real number.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

For each number given, identify whether it is a real number or not a real number: −196 81 .

not a real number real number

Got questions? Get instant answers now!

For each number given, identify whether it is a real number or not a real number: 49 −121 .

real number not a real number

Got questions? Get instant answers now!

Given the numbers −7 , 14 5 , 8 , 5 , 5.9 , 64 , list the whole numbers integers rational numbers irrational numbers real numbers.

Remember, the whole numbers are 0, 1, 2, 3, … and 8 is the only whole number given.
The integers are the whole numbers, their opposites, and 0. So the whole number 8 is an integer, and −7 is the opposite of a whole number so it is an integer, too. Also, notice that 64 is the square of 8 so 64 = −8 . So the integers are −7 , 8 , 64 .
Since all integers are rational, then −7 , 8 , 64 are rational. Rational numbers also include fractions and decimals that repeat or stop, so 14 5 and 5.9 are rational. So the list of rational numbers is −7 , 14 5 , 8 , 5.9 , 64 .
Remember that 5 is not a perfect square, so 5 is irrational.
All the numbers listed are real numbers.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

For the given numbers, list the whole numbers integers rational numbers irrational numbers real numbers: −3 , 2 , 0. 3 , 9 5 , 4 , 49 .

4 , 49 −3 , 4 , 49 −3 , 0. 3 , 9 5 , 4 , 49 2 −3 , 2 , 0. 3 , 9 5 , 4 , 49

Got questions? Get instant answers now!

For the given numbers, list the whole numbers integers rational numbers irrational numbers real numbers: 25 , 3 8 , −1 , 6 , 121 , 2.041975

6 , 121 25 , −1 , 6 , 121 25 , 3 8 , −1 , 6 , 121 2.041975 25 , 3 8 , −1 , 6 , 121 , 2.041975

Got questions? Get instant answers now!

Locate fractions on the number line

The last time we looked at the number line    , it only had positive and negative integers on it. We now want to include fraction    s and decimals on it.

Doing the Manipulative Mathematics activity “Number Line Part 3” will help you develop a better understanding of the location of fractions on the number line.

Let’s start with fractions and locate 1 5 , 4 5 , 3 , 7 4 , 9 2 , −5 , and 8 3 on the number line.

We’ll start with the whole numbers 3 and −5 . because they are the easiest to plot. See [link] .

The proper fractions listed are 1 5 and 4 5 . We know the proper fraction 1 5 has value less than one and so would be located between 0 and 1. The denominator is 5, so we divide the unit from 0 to 1 into 5 equal parts 1 5 , 2 5 , 3 5 , 4 5 . We plot 1 5 . See [link] .

Similarly, 4 5 is between 0 and −1 . After dividing the unit into 5 equal parts we plot 4 5 . See [link] .

Finally, look at the improper fractions 7 4 , 9 2 , 8 3 . These are fractions in which the numerator is greater than the denominator. Locating these points may be easier if you change each of them to a mixed number. See [link] .

Questions & Answers

When traveling to Great Britain, Bethany exchanged $602 US dollars into £515 British pounds. How many pounds did she receive for each US dollar?
Jakoiya Reply
how to reduced echelon form
Solomon Reply
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
Zack Reply
d=r×t the equation would be 8/r+24/r+4=3 worked out
Sheirtina
find the solution to the following functions, check your solutions by substitution. f(x)=x^2-17x+72
Carlos Reply
Aziza is solving this equation-2(1+x)=4x+10
Sechabe Reply
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
KAJAL Reply
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
Adedamola Reply
please the answer to the example exercise
Patricia Reply
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
Edwin Reply
.473
Angelita
?
Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
DaYoungan Reply
p-2/3=5/6 how do I solve it with explanation pls
Adedamola Reply
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
don't understand answer
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
Adedamola Reply
yes
James
don't understand answer
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Rhonda Reply
Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 .
Gabriel Reply
is that a negative 4 or positive 4?
Felix
y = mx + b
Felix
if negative -4, then -4=8/9(0) + b
Felix
-4=b
Felix
if positive 4, then 4=b
Felix
then plug in y=8/9x - 4 or y=8/9x+4
Felix
Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost $6.50 per pound to make?
Cherry Reply
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask