Transcript Scientific Notation - Solon City Schools

Scientific Notation
Helping us write
really tiny
or
really big numbers
Carelessness when using numbers
I have a million math problems to do
 I have a trillion things to get done tonight


If you win 1 million dollars and you’re
given the prize in 100 dollar bills, your
stack of money is….
4 inches high
However…

If you win 1 trillion dollars and you’re
given the prize in 100 dollar bills, your
stack of money is….
67 miles high
Rules to Scientific Notation
Parts:
1. Coefficient (mantissa) – must be a
number from 1 – 9.9
2. Exponent – a power of 10
3.4 x 106
Easier than writing 3,400,000
Numbers Greater Than 10
1.
2.
Find the number by moving the decimal
point that is between 1 – 9.9
45,300,000  4.53
Write a positive exponent which is
equal to the number of places you
moved the decimal point to the left.
4.53 x 107
Numbers Less Than 1
1.
2.
Find the number by moving the decimal
point that is between 1 – 9.9
0.000291  2.91
Write a negative exponent which is
equal to the number of places you
moved the decimal point to the right.
2.91 x 10-4
Math Operations & Sci. Notation
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For Multiplication:
multiply coefficients
add exponents
(3.0 x 104) x (2.0 x 102) = 6.0 x 106
3x2=6
4+2=6
Math Operations & Sci. Notation
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For Division:
divide coefficients
subtract exponents
(6.4 x 106) / (1.7 x 102) = 3.8 x 104
6.4 / 1.7 = 3.8
6–2=4
Be Careful…

Remember the rule about the coefficient!
Ex. (4.0 x 103) x (3.0 x 104) = 12.0 x 107
WRONG!!!
Answer = 1.2 x 108
Math Operations & Sci. Notation

For Addition and Subtraction:
must make the exponents the same
Ex. 5.4 x 103 + 6.0 x 104 =
0.54 x 104
+6.0 x 104
6.5 x 104
Special Note
Sometimes exponents are written
differently.
 We are used to 3.4 x 105
 However, you may see 3.4E5
 It means the same thing (“E” represents
the exponent and replaces x 10
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