8.4 Scientific Notation

8.4 Scientific Notation

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8.4 Scientific Notation

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1. 8.4 Scientific Notation

2. Scientific notation is used to write very large and very small numbers in powers of 10.

3. Decimal formPower of 10Name 1,000,000,000 109 one billion 1,000,000 106 one million 1,000 103 one thousand 100 102 one hundred 10 101 ten 1 100 one .1 10-1 one tenth .01 10-2 one hundredth .001 10-3 one thousandth

4. Form: c  10n where c is a number > 1 and <10 Change decimals to scientific notation: 93,000,000 .00000625 9.3  107 6.25  10-6

5. Scientific Notation to decimal form: 2.83  105 1.5  10-7 283,000 0.00000015

6. Multiplying Scientific notation: (3.2  106) ( 4.2  104) 3.2  4.2  106  104 13.44  1010 1.344  1011 Combine like terms Multiply numbers and add exponents Pull out another positive power of 10, so 1010 + 101 = 1011!

7. Dividing with scientific notation: 4.5  10-7 Divide numbers 9.0  10-4 Subtract exponents .5  10-7-(-4) .5  10-3 5  10-4 .0005 Simplify. or