Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor...
-
Upload
bryan-bryant -
Category
Documents
-
view
221 -
download
2
description
Transcript of Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor...
![Page 1: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/1.jpg)
Exponents: A quick short cut to
multiplication!
74 Means 7 x 7 x 7 x 7
Means 7 is used as a factor 4 times!
![Page 2: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/2.jpg)
74
7 is the base4 is the exponentThe base is used as a factor 4 times.
![Page 3: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/3.jpg)
Expanded notation:5 x 5 x 5 x 5 x 5 x 5
Exponential notation:
56
Evaluated Notation:
15,625
![Page 4: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/4.jpg)
Exponents apply to fractions and decimals too!
2.474 means 2.47 x 2.47 x 2.47x 2.47 &
37.22098(½)4 means
½ x ½ x ½ x ½ &
![Page 5: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/5.jpg)
-54 = ? (-5)4= ? Are they the same?Explain. -24 = ? (-2)4= ? Evaluate both.
![Page 6: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/6.jpg)
(-5)4
Will this value be negative or positive?
(-5)3
Will this value be negative or positive?
Explain.
![Page 7: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/7.jpg)
3 2 x 3 5
Means3 x 3 x 3 x 3 x 3 x 3 x 3
Can you see a short cut?Try it!
54 x 56 = ?27 x 26 =?
![Page 8: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/8.jpg)
72 x 75
7 x 7 x 7 x 7 x 7 x 7 x 7Or77
823,543
![Page 9: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/9.jpg)
We can do this with variables also!
w 3 w 2
w x w x w x w x w
w5
![Page 10: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/10.jpg)
(2a2) (3a5)Apply the commutative property to re-arrange the elements of the
expression.
2 x 3 x a2 x a5 6a7
![Page 11: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/11.jpg)
Power of a Power(63)4
Means this:63∙63∙63∙63
Or
612
![Page 12: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/12.jpg)
(45)2
45 x 45 410
(52)4
52 x 52 x 52 x 52
58
![Page 13: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/13.jpg)
65
63
62 What about this?
75 75-5 = 70
75
1
![Page 14: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/14.jpg)
Therefore anything to the zero power equals
1.
![Page 15: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/15.jpg)
Negative Exponents!5 -3 = 1 53
ab-2 = a b2
12 7 = 12 7-10 = 12-3 = 112 10 123
![Page 16: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/16.jpg)
SCIENTIFIC NOTATION
A QUICK WAY TO WRITE REALLY, REALLY BIG
OR REALLY, REALLY SMALL NUMBERS.
![Page 17: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/17.jpg)
Mathematicians
are Lazy!!!They decided that by
using powers of 10, they can create short versions of long
numbers.
![Page 18: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/18.jpg)
Rules for Scientific Notation
To be in proper scientific notation the number must be written with* a number between 1 and 10* and multiplied by a power of
ten 23 X 105 is not in proper
scientific notation. Why?
![Page 19: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/19.jpg)
Soooo137,000,000 can be
rewritten as
1.37 X 108
![Page 20: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/20.jpg)
Now You TryUsing scientific notation,
rewrite the following numbers.
347,000.3.47 X 105
902,000,000.9.02 X 108
61,400.6.14 X 104
![Page 21: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/21.jpg)
Convert these:
1.23 X 105
123,0006.806 X 106
6,806,000
![Page 22: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/22.jpg)
Try These4,0004 X 103
2.48 X 103
2,4806.123 X 106 6,123,000306,000,0003.06 X 108
![Page 23: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/23.jpg)
In the United States, 15,000,000 households use private wells for
their water supply. Write this number in scientific notation.
1.5 X 107
![Page 24: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/24.jpg)
• The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form.
12,916,000 acres
![Page 25: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/25.jpg)
Why does a Negative Exponent give us a small
number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 101 1 = 100 Do you see a pattern?
![Page 26: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/26.jpg)
Sooooo = 10-1
= = 10-2
= = 10-3
= = 10-4
101
1001
2101
10001
3101
100001
4101
![Page 27: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/27.jpg)
Your TurnUsing Scientific Notation,
rewrite the following numbers.0.0008828.82 X 10-4
0.000000595.9 X 10-7
0.000044 X 10-5
![Page 28: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/28.jpg)
Change to Standard Notation3.89 x 10-5
.0000389
5.074 x 10-9
.000000005074
6.125 x 107
61,250,000
![Page 29: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/29.jpg)
More Examples1) 0.00044 X 10-4
2) 1.248 X 10-6
.0000012483) 6.123 X 10-5
.000061234) 0.000003063.06 X 10-6
5) 0.0008928.92 X 10-4
![Page 30: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/30.jpg)
The nucleus of a human skin cell is about 7 X 10-6 meters in diameter. What is the length in standard notation?
.000007
![Page 31: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/31.jpg)
A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation.
3 X 10-9
![Page 32: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/32.jpg)
Metric System• Napoleon- to unite his empire• Used everywhere except U.S. • Based the number 10• Basic unit of length: meter• Basic unit weight: gram• Basic unit volume: liter
![Page 33: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/33.jpg)
kilo hecto deka unit (meter or liter or gram) deci centi milliTo go down you multiply by ten for each step.To go up you divide by ten for each step.
![Page 34: Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!](https://reader033.fdocuments.us/reader033/viewer/2022052706/5a4d1ad57f8b9ab059972e3d/html5/thumbnails/34.jpg)
Example:Change 7 kilometers to meters: • • = 7,000 meters