1.3 Real Numbers and the Number Line
Transcript of 1.3 Real Numbers and the Number Line
![Page 1: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/1.jpg)
1-3 Real Numbers and the Number Line
I Can:- classify, graph, and compare real
numbers .- find and estimate square roots.
![Page 2: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/2.jpg)
1.OpenerSimplify each of these:
a)
b)
c)
d)
e) Evaluate: for x = 6
f) What number could you evaluate in (e) so that g) What appetizer is most requested with a last meal?
10 (32) ( 22)
( 1)( 1)(1)( 1)(1)( 1)( 1)( 1)( 1)(50)
( 2)(3)( 4)(5)
1 2 3 4 50
x 2 5x 6
x 2 5x 60
![Page 3: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/3.jpg)
Focus Question• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?
![Page 4: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/4.jpg)
Vocabulary to Know • Square Root
• A number a is a square root of a number b if a2 = b
• Example: 72 = 49, so 7 is the square root of 49.
![Page 5: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/5.jpg)
Square Root• You can use the definition of square root to find the exact square roots of some
nonnegative numbers.
• You can approximate the square roots of other nonnegative numbers.
• The radical symbol indicates a nonnegative square root, that is also called the principal square root.
![Page 6: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/6.jpg)
Vocabulary to Know• Radicand
• The expression under the radical symbol is called the radicand.
• x is the radicand in this case
![Page 7: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/7.jpg)
Vocabulary to Know • Radical
• Together, the radical symbol and radicand form a radical.
![Page 8: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/8.jpg)
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
![Page 9: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/9.jpg)
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
![Page 10: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/10.jpg)
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.
![Page 11: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/11.jpg)
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.
• Some types of numbers can be represented on the number line.
![Page 12: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/12.jpg)
Simplifying Square Root Expressions• What is the simplified form of each expression?
![Page 13: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/13.jpg)
Simplifying Square Root Expressions• What is the simplified form of each expression?
![Page 14: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/14.jpg)
Vocabulary to Know• Perfect Square
• The square of an integer
![Page 15: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/15.jpg)
Vocabulary to Know• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
![Page 16: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/16.jpg)
Vocabulary to Know• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
• Copy this list and study it. You will be quizzed.
12 = 1 72 = 49
22 = 4 82 = 64
32 = 9 92 = 81
42 = 16 102 = 100
52 = 25 112 = 121
62 = 36 122 = 144
![Page 17: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/17.jpg)
Estimating a Square Root• Lobster eyes are made of tiny square regions. Under a microscope, the surface
of the eye looks like graph paper. A scientist measure the area of one of the squares to be 386 square microns. What is the approximate side length of the square of the nearest micron?
![Page 18: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/18.jpg)
Estimating Square Root• What is the value of to the nearest integer?
![Page 19: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/19.jpg)
Focus Question Answer• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?
![Page 20: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/20.jpg)
Focus Question• Why is it helpful to classify, graph, and compare numbers?
![Page 21: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/21.jpg)
2.Kinds of Numbers
0natural numbers
0whole numbers
0integers
![Page 22: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/22.jpg)
2.Kinds of Numbers
4 5 6 7 8
51
3
11
2
5.75
rational numbers
3
![Page 23: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/23.jpg)
2.Kinds of Numbers
4 5 6 7 8
irrational numbers
3
15
![Page 24: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/24.jpg)
#1What kind of number is -5?
![Page 25: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/25.jpg)
#1 #2
integer, rational
What kind of number is 42?
What kind of number is -5?
![Page 26: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/26.jpg)
#3#2What kind of number is -4.5669?
What kind of number is 42?
natural, whole, integer, rational
![Page 27: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/27.jpg)
#4#3
rational
Give an example of a positive integer.
What kind of number is -4.5669?
![Page 28: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/28.jpg)
#5#4Give an example of a negative natural number.
Give an example of a positive integer.
![Page 29: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/29.jpg)
#6#5Give an example of a negative natural number.
Give an example of a whole number that isn’t positive.
![Page 30: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/30.jpg)
#7#6Give an example of a whole number that isn’t positive.
What kind of number is most useful to describe:
your shoe size
![Page 31: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/31.jpg)
#8#7
rational
What kind of number is most useful to describe:
your shoe size
What kind of number is most useful to describe:
the temperature in a news report
![Page 32: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/32.jpg)
#9#8
integers
What kind of number is most useful to describe:
the temperature in a news report
What kind of number is most useful to describe:
the number of siblings a person has
![Page 33: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/33.jpg)
#10#9
whole
What kind of number is most useful to describe:
the number of siblings a person has
True or false:
Every rational number is also an integer.
If false, give a counterexample.
![Page 34: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/34.jpg)
#11#10True or false:
Every rational number is also an integer.
If false, give a counterexample.
True or false:
Every whole number is also a natural number.
If false, give a counterexample.
false
![Page 35: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/35.jpg)
#12#11True or false:
Every whole number is also a natural number.
If false, give a counterexample.
True or false:
Every natural number is also a rational number.
If false, give a counterexample.
false
![Page 36: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/36.jpg)
#13#12True or false:
Every natural number is also a rational number.
If false, give a counterexample.
True or false:
Every negative number is also an integer.
If false, give a counterexample.
true
![Page 37: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/37.jpg)
#13True or false:
Every negative number is also an integer.
If false, give a counterexample.true
![Page 38: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/38.jpg)
2.Kinds of Numbers
0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9
8 -6>
![Page 39: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/39.jpg)
2.Kinds of Numbers
0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9
-7 7<
![Page 40: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/40.jpg)
#14-7 10
<
![Page 41: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/41.jpg)
#15#14-7 10 -5 + 10 10 - 5
<
![Page 42: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/42.jpg)
#16#15-5 + 10 10 - 5 10 • 22 2 • 42
=
![Page 43: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/43.jpg)
#1610 • 22 2 • 42
>
![Page 44: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/44.jpg)
Graphing and Ordering Real Numbers• http://
www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-483s.html
![Page 45: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/45.jpg)
Focus Question Answer• Why is it helpful to classify, graph, and compare real numbers?
![Page 46: 1.3 Real Numbers and the Number Line](https://reader034.fdocuments.us/reader034/viewer/2022051016/55895cf6d8b42a643f8b4615/html5/thumbnails/46.jpg)
Your Assignment• Pages 23-25
• 1-5
• 9-17 odd
• 18-34 even
• 35-47 odd
• 48
• 49-59 odd
• 60-64 even
• 66-79