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Unformatted text preview: SCIENTIFIC NOTATION:
Dealing with big and small numbers
Scientiﬁc Notation uses exponentiation.
Exponentiation is repeated multiplication.
For example:
• 104 = 10 ∗ 10 ∗ 10 ∗ 10
• 10−3 = 1
10 ∗ 1
10 ∗ 1
10 Let’s multiply these two numbers:
104 ∗ 10−3 = 10 ∗ 10 ∗ 10 ∗ 10 ∗ 1
1
1
∗
∗
10 10 10 = 10 = 101 It looks like we ended up adding the exponents:
104 ∗ 10−3 = 104+(−3)
= 101 = 10 1 Now let’s divide these two numbers:
104
10−3 = 10 ∗ 10 ∗ 10 ∗ 10
1
1
1
∗ 10 ∗ 10
10 = (10 ∗ 10 ∗ 10 ∗ 10) ∗ (10 ∗ 10 ∗ 10) = 107 It looks like we subtracted the bottom exponent from the top exponent:
104
= 104−(−3) = 104+3 = 107
10−3 What about this?
(102)3 = ? Remember:
Exponentiation is repeated multiplication,
so: (102)3 = (102) ∗ (102) ∗ (102) = 102+2+2 = 106.
So it looks like we ended up multiplying the
exponents:
(102)3 = 102∗3 = 106 2 Some Practice
Let’s evaluate: • 10−4 ∗ 10−3 = 10−7
• 104 ∗ 10−7 = 10−3
10−7 =
• 10−3 10−7−(−3) = 10−4 10−7 ∗ 102 =
• 103 10−11 ∗1024 =
• (106)2 = 10−7−3+2 = 10−8
10−11 ∗1024
(1012 ) 10−11+24−12 = 101 = 10
3 ...
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 Spring '08
 Staff
 Physics, Scientific Notation, operation, Exponentiation, Empty product

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