Numbers & Geometry Constructible Lengths And Irrational Numbers.
Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order...
-
Upload
hilda-simpson -
Category
Documents
-
view
214 -
download
1
Transcript of Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order...
![Page 1: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/1.jpg)
2.1 THE REAL #S AND
ABSOLUTE VALUE
Objective: Compare real numbers.Standards Addressed: 2.1.8.C:
Distinguish between and order rational and irrational numbers.
2.1.8.F: Use the number line model to demonstrate integers and their
applications.
![Page 2: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/2.jpg)
THE REAL NUMBERS: Natural numbers (N) 1, 2, 3, …. Whole numbers (W) 0, 1, 2, 3, …. Integers (Z) …, -3, -2, -1, 0, 1, 2, 3, … Rational numbers (Q) p/q, where p and q
are integers and q ≠ 0. Terminating (2.77) &
repeating (1/3) Irrational numbers (I) #s whose decimal
part doesn’t terminate or repeat (i.e. ∏ )
Real numbers (R) all rational & irrational #s
![Page 3: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/3.jpg)
![Page 4: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/4.jpg)
EX.1 a. 0
R, Q, Z, W
b. ½ R, Q
c. -8 R, Q, Z
d. 8 R, Q, Z, W, N
e. R, I
![Page 5: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/5.jpg)
EX.2 USE DIVISION TO WRITE EACH RATIONAL # AS A DECIMAL & INDICATE WHETHER THE # IS A TERMINATING DECIMAL OR A REPEATING DECIMAL.
a. 4/5
b. 4/11
c. 5/8
d. 7/9
e. 5/12
f. ¾
Terminating
Terminating
Repeating
Repeating
Repeating
Terminating
![Page 6: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/6.jpg)
THE SYMBOLS USED TO COMPARE 2 REAL #S ARE STATED & EXPLAINED BELOW:
< is less than or equal to
> is greater than or equal to
![Page 7: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/7.jpg)
EX. 3
![Page 8: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/8.jpg)
OPPOSITES On the # line, 2 #s that lie on opposite
sides of 0, and are the same distance from 0 are opposites.
The opposite of a negative # is always a positive #.
The opposite of zero is zero itself.
![Page 9: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/9.jpg)
EX. 4 EVALUATE EACH EXPRESSION.
![Page 10: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/10.jpg)
EX. 5 ABSOLUTE VALUE
7 14.2
0 13
![Page 11: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/11.jpg)
![Page 12: Objective: Compare real numbers. Standards Addressed: 2.1.8.C: Distinguish between and order rational and irrational numbers. 2.1.8.F: Use the number line.](https://reader036.fdocuments.us/reader036/viewer/2022082820/56649e375503460f94b27786/html5/thumbnails/12.jpg)