1. Would you be breaking the speed limit in a 40 mi/h zone if you were traveling at 60 km/h?
one kilometer = 0.62 miles
60 km/h = 37.2 mi/h
You would not be speeding!
km/h and mi/h measure the same quantity using different units.

2. Quantitative observation consisting of two parts. number scale (unit)
Nature of Measurement
Quantitative observation consisting of two parts.
number
scale (unit)
Examples
20 grams
6.63 × joule·second

3. The Fundamental SI Units
Physical Quantity
Name of Unit
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
kelvin K
Electric current
ampere A
Amount of substance
mole
mol
Luminous intensity
candela cd

4. Prefixes Used in the SI System
Prefixes are used to change the size of the unit.

5. Prefixes Used in the SI System

6. Practice: In each pair below, circle the larger
Millimeter
Centimeter
picometer
Micrometer
kilogram
Hectogram
deciliter
milliliter

7. Metric System
SI Prefixes
Prefix
Symbol
Meaning
Multiplier
(numerical)
(exponential)
yotta Y
septillion
1,000,000,000,000,000,000,000,000
1024
zetta Z
sextillion
1,000,000,000,000,000,000,000
1021
exa E
quintillion
1,000,000,000,000,000,000
1018
peta P
quadrillion
1,000,000,000,000,000
1015
tera T
trillion
1000,000,000,000
1012
giga G
billion
1,000,000,000
109
mega M
million
1,000,000
106
kilo k
thousand
1,000
103
hecto h
hundred
100
102
deka da
ten 10
101
UNIT
ONE
deci d
tenth
0.1
10-1
centi c
hundredth
0.01
10-2
milli m
thousandth
0.001
10-3
micro 
millionth
10-6
nano 
billionth
10-9
pico 
trillionth
10-12
femto 
quadrillionth
10-15
atto 
quintillionth
10-18
zepto
z ()
sextillionth
10-21
yocto y
septillionth
10-24
When using dimensional analysis for metric problems: always consider the larger unit as having a value of 1, then the smaller unit would contain a large multiple of that unit.
X 1000
X 10
X 10
X 1000
Example: 1 m compared to cm.

8. Factors, ratios, equivalences.
Metric Conversions
SI Prefixes
Prefix
Symbol
Meaning
Multiplier
(numerical)
(exponential)
yotta Y
septillion
1,000,000,000,000,000,000,000,000
1024
zetta Z
sextillion
1,000,000,000,000,000,000,000
1021
exa E
quintillion
1,000,000,000,000,000,000
1018
peta P
quadrillion
1,000,000,000,000,000
1015
tera T
trillion
1000,000,000,000
1012
giga G
billion
1,000,000,000
109
mega M
million
1,000,000
106
kilo k
thousand
1,000
103
hecto h
hundred
100
102
deka da
ten 10
101
UNIT
ONE 1
deci d
tenth
0.1
10-1
centi c
hundredth
0.01
10-2
milli m
thousandth
0.001
10-3
micro 
millionth
10-6
nano 
billionth
10-9
pico 
trillionth
10-12
femto 
quadrillionth
10-15
atto 
quintillionth
10-18
zepto
z ()
sextillionth
10-21
yocto y
septillionth
10-24
Always convert PREFIXES to UNITS (not PREFIXES to other PREFIXES)
Example: Mm compared to pm.
meter, liter, gram
Factors, ratios, equivalences.
Example: cm compared to m.

9. Metric Conversion Problems
LENGTH km hm
dam
METER (m) dm cm mm
2.54 cm = 1 in.
1 mile = 5,280 ft.
1 yd = 36 in.
3 ft. = 1 yard
12 in. = 1 ft.
How many pm are there in cm?
Change 60. mph to km/s. {Hint: 1 mi. = 1.6 km}
How many m3 of water are there in 25 ft3 ? 3 3 3

10. Mass ≠ Weight
Mass is a measure of the resistance of an object to a change in its state of motion. Mass does not vary.
Weight is the force that gravity exerts on an object. Weight varies with the strength of the gravitational field.

11. Mass is the amount of matter, weight is a measure of the gravitational pull on matter

12. Volume: Liter (L) and the milliliter (mL)
10 cm
10 cm
A liter is a cube 1 dm3 = 10 cm long on each side. 10 cm
1 L = dm3 = (10 cm)3 = (10 X 10 X 10) cm3 = 1000 cm3
= 1000 mL or 1mL = 1/1000 L
Cubic centimeter
A milliliter (mL) is a cube 1 cm long on each side.
= milliliter

13. D = Density: m V = A Physical property of a substance, defined as:
Amount of matter (# atoms) per unit volume = compactness.
the mass divided by the volume. =
D = m V
Mass (g)
Volume (mL)

14. Density Problems * For a Fe metal object whose density is 7.86 g/mL.
(a) What is the mass (g) of a piece of this metal if it displaces 12. mL of water in a graduated cylinder?
(b) What is the volume in mL of 34 kg of this same metal?

15. *
Density Problems
The density of Hg is 11.7 g/mL. What is it in kg/m3? 3

16. *
Temperature: measure of the average kinetic energy (motion caused by heat) of the particles in a sample.
{K.E ∝ Temp}
T = change in temp
As KE increases molecules vibrate more and their volume expands (Temp).
373
273
100
100
- 0
212 32
180
C = (F − 32)
1.8
F = 1.8(C) + 32
K = C

17. Dimensional Analysis !Remeber!
Use when converting a given result from one system of units to another.
To convert from one unit to another, use the equivalence statement that relates the two units.
Derive the appropriate unit factor by looking at the direction of the required change (to cancel the unwanted units).
Multiply the quantity to be converted by the unit factor to give the quantity with the desired units.

18. English and Metric Conversions
If you know ONE conversion for each type of measurement, you can convert anything!
You must memorize and use these conversions:
Mass: 454 grams = 1 pound
Length: cm = 1 inch
Volume: L = 1 quart

19. A golfer putted a golf ball 6. 8 ft across a green
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
Example #1
To convert from one unit to another, use the equivalence statement that relates the two units.
1 ft = 12 in
The two unit factors are:

20. Example #1
A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent?
Derive the appropriate unit factor by looking at the direction of the required change (to cancel the unwanted units).
Multiply the quantity to be converted by the unit factor to give the quantity with the desired units.

21. Example #2
An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams?
(1 kg = lbs; 1 kg = 1000 g)

22. ( ) Square and Cubic units 4.3 cm3 10 mm 3 1 cm 4.3 cm3 103 mm3 13 cm3
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the ENTIRE conversion factor
Example: Convert 4.3 cm3 to mm3
4.3 cm mm 3
1 cm
4.3 cm mm3
13 cm3
( ) =
= 4300 mm3

23. CONCEPT CHECK!
What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation.
This problem requires that the students think about how they will solve the problem before they can plug numbers into an equation. A sample answer is:
Distance between New York and Los Angeles: miles
Average gas mileage: 25 miles per gallon
Average cost of gasoline: $2.75 per gallon
(3200 mi) × (1 gal/25 mi) × ($2.75/1 gal) = $352
Total cost = $350

24. At what temperature does °C = °F?
EXERCISE!
At what temperature does °C = °F?
Since °C equals °F, they both should be the same value (designated as variable x).
Use one of the conversion equations such as:
Substitute in the value of x for both TC and TF. Solve for x.
The answer is -40. Since °C equals °F, they both should be the same value (designated as variable x). Use one of the conversion equations such as °C = (°F-32)(5/9), and substitute in the value of x for both °C and °F. Solve for x.

25. EXERCISE!

26. Ex. 2) The volume of water in a graduated cylinder is 27. 0 mL
Ex. 2) The volume of water in a graduated cylinder is 27.0 mL. A piece of lead is slowly dropped into the cylinder giving the volume to become mL. Given that lead’s density is 11.3g/cm3 what is the mass of Pb? Ex. 3) An empty beaker has a mass of 25.83g. When it is filled with mercury, it’s new mass is 225.3g. If the density of mercury is g/cm3, what is the volume of the beaker?

27. How big is the beetle? Measure between the head and the tail!
Between 1.5 and 1.6 in
Measured length: 1.54 in
The 1 and 5 are known with certainty
The last digit (4) is estimated between the two nearest fine division marks.
Copyright © by Fred Senese

28. Uncertainty in measurements
A digit that must be estimated in a measurement is called uncertain.
A measurement always has some degree of uncertainty. It is dependent on the precision of the measuring device.
Record the certain digits and the first uncertain digit (the estimated number).

29. Measurement of Volume Using a Buret
The volume is read at the bottom of the liquid curve (meniscus).
Meniscus of the liquid occurs at about mL.
Certain digits: 20.15
Uncertain digit: 20.15

31. Precision and Accuracy
Agreement of a particular value with the true value.
Precision
Degree of agreement among several measurements of the same quantity.

32. Precision and Accuracy
Which would you prefer to be ? Precise or Accurate?

33. Precision and Accuracy

34. Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures.
3456 has 4 sig figs (significant figures).
2. There are three classes of zeros.
a. Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures.
0.048 has 2 sig figs.

35. Rules for Counting Significant Figures
Classes of zeros.
b. Captive zeros are zeros between nonzero digits. These always count as significant figures.
16.07 has 4 sig figs.
c. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point.
9.300 has 4 sig figs.
150 has 2 sig figs.

36. Rules for Counting Significant Figures
3. Exact numbers have an infinite number of significant figures.
1 inch = 2.54 cm, exactly.
9 pencils (obtained by counting).

37. Exponential Notation Example Two Advantages 300. written as 3.00 × 102
Contains three significant figures.
Two Advantages
Number of significant figures can be easily indicated.
Fewer zeros are needed to write a very large or very small number.

38. Significant Figures in Mathematical Operations
1. For multiplication or division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation.
1.342 × 5.5 =  7.4

39. Significant Figures in Mathematical Operations
2. For addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation.

40. CONCEPT CHECK!
You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).
How would you write the number describing the total volume?
= 3.1 mL
What limits the precision of the total volume?
The total volume is 3.1 mL. The first graduated cylinder limits the precision of the total volume with a volume of 2.8 mL. The second graduated cylinder has a volume of 0.28 mL. Therefore, the final volume must be 3.1 mL since the first volume is limited to the tenths place.