4.4 Scientific Notation.notebook
September 15, 2011
4.4 Scientific Notation
­used to represent large and small numbers
4.73 x 105
The power of ten is determined by how many places the decimal is moved when changing a number to scientific notation. The positive powers of ten represent larger numbers. The negative powers of ten are used to represent decimals between 0 and 1, such as .0000045
Sep 14­11:17 AM
Write each number in scientific notation.
0.000003
45,780,000
0.00000405
607,000
5,700
.000037
.00028
4,050,000
Sep 14­12:00 PM
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4.4 Scientific Notation.notebook
September 15, 2011
So when the decimal point was moved left to change a larger number into scientific notation, the power of ten went up or was positive. When the decimal point moved to the right to change a small decimal into scientific notation, the power of ten went down or was negative.
Sep 15­5:28 PM
Write each number in standard notation
4 x 10­7
3.2 x 108
4.05 x 10­5
1.003 x 102
Changing a number back to standard form from scientific notation means that you need to get rid of the power of ten (by making it zero) by moving the decimal point to the right or left. By moving the decimal point to the left, the power of ten goes up (gets rid of negative powers). By moving the decimal point to the right, the power of ten goes down (gets rid of positive powers).
Sep 14­12:00 PM
2
4.4 Scientific Notation.notebook
September 15, 2011
Write the numbers in scientific notation
12.5 x 10­4
35 x 105
0.00001001
0.0004 x 10­3
For changing a number that is not in correct scientific notation to scientific notation you could change it to standard notation and then scientific notation as shown in the first two examples above. The other option is moving the decimal point and increasing the power of ten if you move the decimal point to the left, and decreasing the power of ten if you move the decimal point to the right.
Sep 14­12:00 PM
Which number is larger for each pair?
4 x 10­3 or 3.7 x 10­2
2.54 x 10­5 or 3.1 x 10­5
4.001 x 1018 or 4.07 x 1018
The number with the larger power of ten is larger if both numbers are in scientific notation. If both numbers are in scientific notation and have the same power of ten, then you look to see which has a larger number preceding the power of ten.
Sep 14­12:00 PM
3
4.4 Scientific Notation.notebook
September 15, 2011
HW 4.4 p176 #1­20
Sep 14­12:00 PM
4