1. Expressing Measurements
Scientific notation
A number is written as the product of two numbers
A coefficient
10 raised to a power
Example: Put IN Scientific Notation
A. 602,000, B C
6.02x x x100

2. Expressing Measurements
Example: Put OUT of Scientific Notation A x104 B x , Example: Put in CORRECT Scientific Notation A x103 B x x x10-1

3. Scientific Measurement
Measurement depends on
Accuracy (“Correctness”)
A measure of how close a
measurement comes to the actual
or true value of whatever is measured
Precision (“Reproducibility”)
A measure of how close a series of
measurements are to one another
Examples:

4. Scientific Measurement
Measurement is never certain because measurement instruments are never free of flaws.
So we only count numbers that are SIGNIFICANT
***All certain numbers plus one uncertain number***

5. Rules for Counting SIG FIGS
NON ZERO INTERGERS: are ALWAYS significant Examples: mL = _____ sig figs 62 in. = _____ sig figs 43, g = _____ sig figs

6. Rules for Counting SIG FIGS
2. ZEROS (There are three classes) LEADING ZEROS are NEVER significant Examples: .034 g = _____ sig figs m = _____ sig figs

7. Rules for Counting SIG FIGS
B. CAPTIVE ZEROS are ALWAYS significant Examples: 205 mi = _____ sig figs 10,005 g = _____ sig figs

8. Rules for Counting SIG FIGS
C. TRAILING ZEROS are SOMETIMES significant.
Only when there is a decimal point*
Examples:
16,000 mi = _____ sig figs
16,000.0 mi = _____ sig figs
m = _____ sig figs

9. Rules for Counting SIG FIGS
3. EXACT NUMBERS are INFINATELY significant Examples: Counting students Conversions

10. OPERATIONS & SIG FIGS
“The result of calculations involving measurements can only be as precise as the least precise measurement”

11. OPERATIONS & SIG FIGS 1. MULTIPLICATION AND DIVISION
The product (x) or quotient (/) contain the same number of sig figs as the measurement with the least number of sig figs.
Example:
24 cm x 31.8 cm = cm2  760 cm2

12. OPERATIONS & SIG FIGS 2. ADDITION AND SUBTRACTION
The sum or difference has the same number of decimal places as the number with the least decimal places.
Examples:
7.52 cm cm = cm  16.2 cm
39 m m = m  40. m

13. Metric System
History – people did not have measuring devices readily available
English (customary units)
Foot = length of king’s foot at the time
Inch = length between 1st & 2nd knuckles
Pound (lb) = “Liberty” or “Justice” used to measure grains
Metric
Meter – originally 1/10,000,000 of distance from North Pole to equator
Gram – weight of 1 cm3 block and 1cc of H2O in syringe
Liter = 1,000 cm3

14. SI Units Treaty in 1875 to come up with standard system Basic SI Units
International System of Measurements (SI)
French: Le Système international d'unités
Basic SI Units
Length = meter (m)
Mass = kilogram (kg); gram is too small to use as basic unit
Time = seconds (s)
Electric current = ampere (amp)
Temperature = Kelvin (K); never use °K; based on absolute zero
Amount of a substance = mole (mol)
Luminous intensity = candela
All other units are derived from these 7 basic units

15. Area = l × w = m × m
Denisty = mass/volume = kg/l × w × h (m × m × m)
psi = lb/in2  kg/m

16. Metric Prefixes (example: density kg/m3) Basic Units
Mass = gram (g)
Length = meter (m)
Volume = liter (L)
There are three major parts to the metric system:
the seven base units (example: meters)
the prefixes (example: kilometer)
units built up from the base units.
(example: density kg/m3)

17. Prefix Symbol Numerical Exponential
tera T 1,000,000,000,
giga G 1,000,000,
mega M ,000,
kilo k ,
hecto h
Deka da
Unit No prefix (m, L, g)

18. Prefix Symbol Numerical Exponential
deci d
centi c
milli m
micro 
nano n
pico p

19. Putting it All Together
1 kilometer = 1 x 103 m = 1000 m
1 picometer = 1 x m = m
1 milligram = 1 x 10-3 g = g

20. Need to know all the units, especially k h d u d c m
Note: There are units between these numbers (i.e., 10-4, 10-5, etc.) but they don’t have a prefix, so we don’t discuss them
Need to know all the units, especially
k h d u d c m
“King Henry drinks up delicious chocolate milk.”

21. Metric Conversions memorize the metric prefixes names and symbols.
determine which of two prefixes represents a larger amount.
determine the exponential "distance" between two prefixes.

22. Practice! 22.6 mm = _______ m .61 gh = _____ cg 78.5 mL = _____ L
Answer: m (already in correct # of sig figs)
.61 gh = _____ cg
Answer: 6100 cg
78.5 mL = _____ L
Answer: L

23. Memorize These!!! 1 L = 1 dm3 1 mL = 1 cm3
dm3 used for solid volume; L or mL used for liquid volume
1 mL = 1 cm3
1 mL of H2O = 1 g = 1 cm3 (a.k.a., “cc” in hospitals)

24. These are Tricky Ones
Whenever you see squares or cubes, slow down and handle the problem differently
12.0 cm2 = _____ mm2
Answer: 1200 mm2
21 mL = _____ cm3
Answer: 21 cm3

25. Just for Fun 5.82 mm = ______ Tm 35.2 dm2 = _____ hm2
2.79 L = _____dm3
45 km/min = _____ m/s
Hardest one I can give you (no setup = no credit):
3 weeks = _____ s