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Moving from Sig Figs to Scientific Notation Scientific notation • Begin with 1230000 • Move the decimal point six places to the left yielding • 1230000. Scientific notation • Begin with 1230000 • Move the decimal point six places to the left yielding • 1.230000 • 1.23 x 106 Scientific notation • Start with 0.000000456 • Move the decimal point seven places to the right yielding • 0.000000456 Scientific notation • Start with 0.000000456 • Move the decimal point seven places to the right yielding • 0 0000004.56 • 4.56 x 10-7 Rules for Multiplication in Scientific Notation • • • • • 1) Multiply the coefficients 2) Add the exponents (base 10 remains) Example - (3 x 104)(2 x 105) = 9 6 x 10 3 4 (2 x 10 )(4 x 10 )= 7 5 6 8 x 10 (6 x 10 )(7 x 10 )= 42 x 1011 4.2 x 1012 Rules for Addition and Subtraction in Scientific Notation • When adding or subtracting in scientific notation, you must express the numbers as the same power of 10 • This will often involve changing the decimal place of the coefficient. • (3.76 x 104) + (5.5 x 102) = • (3.76 x 104) + (0.055 x 104) = 3.815 x 104 • 37600 + 550 = 38150 Rules for Addition and Subtraction in Scientific Notation • When adding or subtracting in scientific notation, you must express the numbers as the same power of 10 • This will often involve changing the decimal place of the coefficient. • (4.8 x 105) - (9.7 x 104) = 3.83 x 105 • (4.8 x 105) - (0.97 x 105) = • 480000 - 97000 = 383000 Dividing with Scientific Notation • When dividing with scientific notation, divide the coefficients and subtract the exponents. The base will remain 10. • Example: 3.5 x 108 ÷ 6.6 x 104 .530303 x 104 5.3 x 103