Post on 13-Dec-2015
Practice:
a) 27.68 cm –14.369 cm =b) 6.54 m x 0.37 m =c) 40.8 m2 ¸ 5.050 m =
Practice:
a) 27.68 cm –14.369 cm = 13.311 13.31b) 6.54 m x 0.37 m = 2.4198 2.4c) 40.8 m2 ¸ 5.050 m = 8.07921 8.08
Raw Math Value
Sig. Fig. Value
Scientific
Notation
Thursday, August 13th, 2015
Textbook pages 63 –
65
Scientific Notation
Scientific notation is way of writing numbers that are too big or too small to be conveniently written in decimal form
Rules for Scientific Notation
To be in proper scientific notation the number must be written with
* a number between 1 and 10
* and multiplied by a power of
ten
23 X 105 is not in proper scientific notation. Why?
1. Move the decimal to the right of the first non-zero
number.2. Count how many places the
decimal had to be moved.3. If the decimal had to be moved
to the right, the exponent is negative.
4. If the decimal had to be moved to the left, the exponent is positive.
To write a number in scientific notation:
BIGExamples!
300 = 3 x 102
60,000 = 6 x 104
98,000,000 = 9.8 x 107
8657 = 8.657 x 103
250 =
36,700 =
785,000,000 =
99,000,000,000 =
Try
These
4,000
2.48 X 103
6.123 X 106
306,000,000
5.70 x 105
Convert each from scientific notation into standard/long form or vice versa
small
Examples!
0.02 = 2 x 10-2
0.0065 = 6.5 x 10-3
0.0000708 = 7.08 x 10-5
0.000000001 = 1 x 10-9
0.25 =
0.0036 =
0.00007001 =
0.00000003 =
Why does a Negative Exponent give us a small
number?
10000 = 10 x 10 x 10 x 10 = 104
1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 101
1 = 100
Do you see a pattern?
Try
These0.00873
3.48 X 10-4
0.156
0.00000099
5.70 x 10-6
Convert each from scientific notation into standard/long form or vice versa
10,003 9.57 x 10-7
1.6 x 103 507,000,000
0.0001 3.301 x 105
6.1 x 1010 1.8 x 10-9
10,000,000,000 0.0045
Convert each from scientific notation into standard/long form or vice versa
Multiplication
When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5
Answer: 6.7 x 102
DivisionDivide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.Sample Problem: Divide (6.4 x 106) by (1.7
x 102)Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2
Answer: 3.8 x 104
Addition and SubtractionTo add or subtract numbers written in
scientific notation, you must….express them with the same power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)Solution: Since the two numbers are not
expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.
5.8 x 103 = .58 x 104 so .58 x 104 + 2.16 x 104 =?Answer: 2.74 x 104