1. Find your Notecard Partner. Why would we use scientific notation?

2. What is the Length? We can see the markings between 1.6-1.7cm
We can’t see the markings between the .6-.7
We must guess between .6 & .7
We record 1.67 cm as our measurement
The last digit an 7 was our guess...stop there

3. Learning Check What is the length of the wooden stick? 1) 4.5 cm

4. Measurement and Significant Figures
Every experimental measurement has a degree of uncertainty.
The volume, V, at right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.
Chapter Two

5. REALLY, REALLY SMALL NUMBERS.
SCIENTIFIC NOTATION
A QUICK WAY TO WRITE
REALLY, REALLY BIG OR
REALLY, REALLY SMALL NUMBERS.

6. 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?

7. 0.0000187 370,000,000 78.8 0.02164 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
78.8

8. Change to scientific notation.
12,340 =
0.369 =
0.008 =
1,000. =
1.234 x 104
3.69 x 10–1
8 x 10–3
1.000 x 103

9. NEED TO KNOW Prefixes in the SI System
Power of 10 for
Prefix Symbol Meaning Scientific Notation
_________________________________________________________
mega- M ,000,
kilo- k ,
deci- d
centi- c
milli- m
micro- m
nano- n
pico- p

10. Significant figures ??? Method used to express accuracy and precision.
You can’t report numbers better than the method used to measure them.
67.20 cm = four significant figures
???
Certain
Digits
Uncertain
Digit

11. The number of significant digits is independent of the decimal point.
Significant figures
The number of significant digits is independent of the decimal point.
255
31.7
5.60
0.934
0.0150
These numbers
All have three
significant figures!

12. Rules for Counting Significant figures
Every non-zero digit is ALWAYS significant!
Zeros are what will give you a headache!
They are used/misused all of the time.
SEE p.24 in your book!

13. Rules for zeros Leading zeros are not significant. ???
Captive zeros are always significant!
three significant figures
Leading zero
???
4,008 - four significant figures
Captive zeros
???
Trailing zeros are significant …
IF there’s a decimal point in the number!
five significant figures
Trailing zero
???

14. Examples 250 mg \__ 2 significant figures 120. mileskg
23, s
\__ 7 significant figures

15. Significant figures: Rules for zeros
Scientific notation - can be used to clearly express significant figures.
A properly written number in scientific notation always has the proper number of significant figures.
= x 10-3
Three Significant
Figures

16. Significant figures and calculations
An answer can’t have more significant figures than the quantities used to produce it.
Example
How fast did you run if you
went 1.0 km in 3.0 minutes?
speed = 1.0 km
3.0 min
= 0.33 km
min

17. Significant figures and calculations
Multiplication and division.
Your answer should have the same number of sig figs as the original number with the smallest number of significant figures.
ONLY 3 SIG FIGS!
21.4 cm x cm = 66.2 cm2
135 km ÷ 2.0 hr = 68 km/hr
ONLY 2 SIG FIGS!

18. Significant figures and calculations
Addition and subtraction
Your answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with. g g g
805.4 g g
83.7 g

19. Rounding off numbers
After calculations, you may need to round off.
If the first insignificant digit is 5 or more, you round up
If the first insignificant digit is 4 or less, you round down.

20. Examples of rounding off
If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then -
becomes
becomes
1st insignificant digit

21. Examples of Rounding For example you want a 4 Sig Fig number
0 is dropped, it is <5
8 is dropped, it is >5; Note you must include the 0’s
5 is dropped it is = 5; note you need a 4 Sig Fig
780,582
1999.5
4965
780,600
2000.

22. Multiplication and division
 1.54 =
3.68  =
1.750  =
3.2650106  =  107
6.0221023  1.66110-24 =
49.7
46.4
.05985
1.586 107
1.000