Transcript Slide 1

Aim: How can we convert
numbers into scientific notation
and help with significant figures?
Do Now
The speed of light is 300,000,000 m/s
How would this look in scientific notation?
The answer will be known shortly
SCIENTIFIC NOTATION
Illustrates numbers by orders of magnitude (Powers of 10)
100 =
1
10-1 =
0.1 or 1/10
101 =
10
10-2 =
0.01 or 1/100
102 =
100
10-3 =
0.001 or 1/1,000
Scientific Notation Form:
M x 10n
Rules:
1. M must only have 1 non-zero digit to the left of the
decimal.
Example: 3.24 x 102 is correct
32.4 x 101 is incorrect
0.324 x 103 is incorrect
2. Add a power of 10 every time you move the decimal
point one place to the left
Example: 45,625 (this is really 45,625 x 100)
4
32 1
4.5625 x 104
3. Subtract a power of 10 every time you move the
decimal point one place to the right
Example: 0.00538 (this is really 0.00538 x 100)
1 2
3
5.38 x 10-3
Do Now: 300,000,000 x 100 = 3.0 x 108
Who was right?
Convert the following to standard notation:
1) 5.5 x 104
55,000
2) 8.321 x 10-3
0.008321
3) 2.1 x 109
2,100,000,000
4) 3.8 x 10-5
0.000038
Convert the following to scientific notation:
5) 9,508
9.508 x 103
6) 0.000607
6.07 x 10-4
7) 10,501
1.0501 x 104
8) 0.025
2.5 x 10-2
Only reliable accurate digits can be in scientific
notation.
These are known as significant digits (significant
figures)
Rules:
1. All non-zero digits are significant
Ex: 112.832
6 sig. figs.
2. All zeros between non-zeros are significant
Ex: 1003.01
6 sig. figs.
3. All final zeros before a decimal and beginning zeros are
not significant
Ex: 300,000,000
1 sig. fig.
0.000098
2 sig. figs.
4. All final zeros after a decimal are significant
Ex: 25.00
4 sig. figs.
How many sig. figs. are in each of the following:
1. 9,500
2
2. 0.0090080
5
3. 10,201.06
7
4. 6.2 x 106
2
Take out your calculators
Do you know how to use your calculator correctly?
Your calculator has a button that either says EE or
EXP
This button means times ten to the
Ex: 3.97 x 1014 x 2.86 x 10-17 =
This is how you type it:
3.97 EE 14 x 2.86 EE ± 17 =
or
3.97 EXP 14 x 2.86 EXP (-) 17 =
Pages for Additional Reading
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Pages 28, 31