laws of exponents scientific notation created by: angie gallacher james workman middle school palm...
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Laws of Exponents
Scientific Notation
Created By:Angie Gallacher
James workman Middle SchoolPalm Springs Unified School District
http://angiegallacher.googlepages.com/
Product of Powers Property
•To multiply powers (exponents) with the same base, add their exponents.
a³ x a²= a3 + 2 = a5
25
23=
2 x 2 x 2 x 2 x 2
2 x 2 x 2= 22
1
45
42=
4 x 4 x 4 x 4 x 4
4 x 4=
43
1
Do you see a pattern or shortcut?
Quotient of Powers Property
•To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator.
68 = 68-5 =63
65
Zero Exponents•For any nonzero number a, a0 = 1
•Anything to the zero power equals 1 (except zero)
40 =1000 = 1
1
Write in scientific notation.
46,200,000,000 =
4.62 x 109
Where is the decimal now?
Move the decimal to the right of the first significant digit.
Write in scientific notation.
89,000,000 = 8.9 x 107
Where is the decimal now?
Move the decimal to the right of the first significant digit.
Write in scientific notation.
304,000,000,000 =
3.04 x 1011
Where is the decimal now?
Move the decimal to the right of the first significant digit.
Write in scientific notation.
0.00000052 = 5.2 x 10-7
Move the decimal to the right of the first significant digit.
# is less than 1 so exponent is negative
Write in scientific notation.
0.00000000106 =
1.06 x 10-9
Move the decimal to the right of the first significant digit.
# is less than 1 so exponent is negative
3.2 x 107 =
Positive Exponents move the decimal to the right
3 2 0 0 0 00 0
Write in standard form.
Count the # of spaces to move and fill in with zeros.
6.04 x 105=
Positive Exponents move the decimal to the right
6 0 40 0 0
Write in standard form.
Count the # of spaces to move and fill in with zeros.
1.3 x 10-5 =
Negative Exponents move the decimal to the left. # less than 1.
1 300 00
Write in standard form.
Count the # of spaces to move left and fill in with zeros. Then add a decimal point
2.07 x 10-4 =
Negative Exponents move the decimal to the left. # less than 1.
2 0 700 0
Write in standard form.
Count the # of spaces to move left and fill in with zeros. Then add a decimal point
Write these in scientific notation.
4100 4.1 x 103
0.000067 6.7 x 10-5
62,000,000 6.2 x 107
0.000000003 3 x 10-9
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