2. 8.4 Scientific Notation

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

4. Decimal formPower of 10Name 1,000,000,00010 9 one billion 1,000,00010 6 one million 1,00010 3 one thousand 10010 2 one hundred 1010 1 ten 110 0 one.110 -1 one tenth.0110 -2 one hundredth.00110 -3 one thousandth

5. Form: c  10 n where c is a number > 1 and <10 Change decimals to scientific notation: 93,000,000.00000625 9.3  10 7 6.25  10 -6

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

7. Multiplying Scientific notation: (3.2  10 6 ) ( 4.2  10 4 ) 3.2  4.2  10 6  10 4 13.44  10 10 1.344  10 11 Combine like terms Multiply numbers and add exponents Pull out another positive power of 10, so 10 10 + 10 1 = 10 11 !

8. Dividing with scientific notation: 4.5  10 -7 9.0  10 -4.5  10 -7-(-4).5  10 -3 5  10 -4.0005 Divide numbers Subtract exponents Simplify. or