Post on 26-Mar-2015
Why is thisstuff important?
Scientific Notation
Often used to express
very large or
very small numbers.
Also used to maintain
correct number of
significant figures.
Form: (# from 1 to 9.999) x 10exponent
800 = 8 x 10 x 10
= 8 x 102
2531 = 2.531 x 10 x 10 x 10
= 2.531 x 103
0.0014 = 1.4 / 10 / 10 / 10
= 1.4 x 10-3
Change to standard form.
1.87 x 10–5 =
3.7 x 108 =
7.88 x 101 =
2.164 x 10–2 =
370,000,000
0.0000187
78.8
0.02164
000000187000000..
Change to scientific notation.
12,340 =
0.369 =
0.008 =
1,000,000,000 =
1.234 x 104
3.69 x 10–1
8 x 10–3
1 x 109
Using the Exponent Key
on a Calculator
EXP
EE2nd
EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023:
6 EE. 0 32 2
How to type out 6.02 x 1023:
6 EE. 0 32 2
Also, know when to hit your (–) sign…
…before the number,
…after the number,
…or either one.
Example:1.2 x 105 2.8 x 1013
But instead is written…
=
1 . 2 EE 5
32 . 8 EE 1
Type this calculation in like this:
This is NOT written… 4.3–9
4.2857143 –09Calculator gives…
4.2857143 E–09or…
4.3 x 10–9 4.3 E –9or
2nd
2nd
3-6 10 x 1.23 10 x 4.35
4-6- 10 x 8.7- 10 x 7.5
4-16- 10 x 9.86 10 x 5.76
1111 10 x 3.3 10 x 8.8
= -6.525 x 10-9
= 5.3505 x 103 or 5350.5
= 5.84178499 x 10-13
report -6.5 x 10-9 (2 sig. figs.)
report 5.35 x 103 (3 sig. figs.)
report 5.84 x 10-13 (3 sig. figs.)
= 2.904 x 1023
report 2.9 x 1023 (2 sig. figs.) 8-23 10 x 5.1- 10 x 6.022 = -3.07122 x 1016
report -3.1 x 1016 (2 sig. figs.)
(–)
Rule for MultiplicationCalculating with Numbers Written in Scientific Notation
When multiplying numbers in scientific notation, multiply thefirst factors and ADD the exponents.
Sample Problem: Multiply (3.2 x 10-7 )x (2.1 x 105)
(3.2) x (2.1) = 6.72
(-7) + (5) = -2 or 10-2
6.72 x 10-2
Exercise: Multiply (14.6 x 107 ) X (1.5 x 104 ) 2.19 x 1012
Rule for DivisionCalculating with Numbers Written in Scientific Notation
When dividing numbers in scientific notation, divide the first factor in the numerator by the first factor in the denominator.Then subtract the exponent in the denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106 ) by (1.7 x 102 )
(6.4) (1.7) = 3.76
(6) - (2) = 4 or 104
3.76 x 104
Exercise: Divide 2.4 x 10-7 by 3.1 x 1014 7.74 x 10-22
..
Rule for Addition and SubtractionCalculating with Numbers Written in Scientific Notation
In order to add or subtract numbers written in scientific notation, you must express them with the same power of 10.
Sample Problem: Add (5.8 x 103 ) + ( 2.16 x 104 )
(5.8 x 103) + (21.6 x 103) = 27.4 x 103
Exercise: Add (8.32 x 10-7 ) + (1.2 x 10-5 ) 1.28 x 10-5
2.74 x 104
Using Scientific Notation for Expressing the Correct Number of Significant Figures
Measurement Number of significant figures it contains
Measurement Number of significant figures it contains
25 g
0.030 kg
1.240560 x 106 mg
6 x 104 sec
246.31 g
20.06 cm
1.050 m
0.12 kg
1240560. cm
6000000 kg
6.00 x 106 kg
409 cm
29.200 cm
0.02500 g
2
2
7
1
5
4
4
2
7
1
3
3
5
4