Transcript Measurement powerpoint

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. 602,000,000
B. 0.00774560
6.02x108
7.74560 x10-3
C. 2.753
2.753 x100
Expressing Measurements
Example: Put OUT of Scientific Notation
A. 3.51 x104
B. 5.001 x10-5
35,100
.00005001
Example: Put in CORRECT Scientific Notation
A. 237.1 x103
B. 43578.1 x10-5
2.317 x105
4.35781 x10-1
Scientific Measurement
 Measurement depends on
1.
Accuracy (“Correctness”)
A measure of how close a
measurement comes to the actual
or true value of whatever is measured
2. Precision (“Reproducibility”)
A measure of how close a series of
measurements are to one another
Examples:
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***
Rules for Counting SIG FIGS
NON ZERO INTERGERS: are ALWAYS significant
Examples:
352.1 mL = _____ sig figs
62 in. = _____ sig figs
43,978.6821g = _____ sig figs
Rules for Counting SIG FIGS
2. ZEROS (There are three classes)
LEADING ZEROS are NEVER significant
Examples:
.034 g = _____ sig figs
0.0006178 m = _____ sig figs
Rules for Counting SIG FIGS
B. CAPTIVE ZEROS are ALWAYS significant
Examples:
205 mi = _____ sig figs
10,005 g = _____ sig figs
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
2.3500 m = _____ sig figs
Rules for Counting SIG FIGS
3. EXACT NUMBERS are INFINATELY significant
Examples:
Counting students
Conversions
OPERATIONS & SIG FIGS
“The result of calculations involving measurements can
only be as precise as the least precise measurement”
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 = 763.2 cm2  760 cm2
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 + 8.7 cm = 16.22 cm  16.2 cm
39 m + 0.7893 m = 39.7893 m  40. m
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

SI Units
 Treaty in 1875 to come up with standard system
 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
 Area = l × w = m × m
 Denisty = mass/volume = kg/l × w × h (m × m × m)
 psi = lb/in2  kg/m
Metric Prefixes
 Basic Units
 Mass = gram (g)
 Length = meter (m)
 Volume = liter (L)
There are three major parts to the metric system:
1. the seven base units (example: meters)
2. the prefixes (example: kilometer)
3. units built up from the base units.
(example: density kg/m3)
Prefix Symbol
Numerical
tera
T
1,000,000,000,000
giga
G
1,000,000,000
mega
M
1,000,000
kilo
k
1,000
hecto
h
100
Deka
da
10
Unit
No prefix (m, L, g) 1
Exponential
1012
109
106
103
102
101
100
Prefix Symbol
deci
d
centi
c
milli
m
micro

nano
n
pico
p
Numerical
Exponential
0.1
10-1
0.01
10-2
0.001
10-3
0.000001
10-6
0.000000001
10-9
0.000000000001
10-12
Putting it All Together
 1 kilometer = 1 x 103 m = 1000 m
 1 picometer = 1 x 10-12 m = 0.000000000001 m
 1 milligram = 1 x 10-3 g = 0.001 g
 Note: There are units between these numbers (i.e., 104,
10-5, etc.) but they don’t have a prefix, so we don’t
discuss them
 Need to know all the units, especially
 khdudcm
 “King Henry drinks up delicious chocolate milk.”
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.
Practice!
 22.6 mm = _______ m
 Answer: 0.0226 m (already in correct # of sig figs)
 .61 gh = _____ cg
 Answer: 6100 cg
 78.5 mL = _____ L
 Answer: 0.0785 L
Memorize These!!!
 1 L = 1 dm3

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)
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
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