Transcript Moving from Sig Figs to Scientific Notation

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
•
•
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•
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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