Big_Small_Numbers - SCIENTIFIC NOTATION: Dealing with big...

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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 = • 104 ∗ 10−7 = 10−7 = • 10−3 10−7 ∗ 102 = • 103 10−11 ∗1024 = • (106)2 3 ...
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This note was uploaded on 10/19/2011 for the course PHY 2020 taught by Professor Staff during the Spring '08 term at University of Florida.

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Big_Small_Numbers - SCIENTIFIC NOTATION: Dealing with big...

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