2. Intro problems: D = m
V
• Calculate the density of a piece of bone
with a mass of 3.8 g and a volume of 2.0
cm3
• A spoonful of sugar with a mass of 8.8
grams is poured into a 10 mL graduated
cylinder. The volume reading is 5.5 mL.
What is the density of the sugar?
3. Not so long ago…….
People used all kinds of units to describe
measurements:
Their feet
Sundials
The length of their arm
4. Needless to say, this led to much
confusion!
• Scientist needed a way to report their
findings in a way that everyone else
understood.
• So, in 1795, the French developed a system
of standard units, which was updated in
1960
• The revised system is called the Système
Internationale d’Unités, which is
abbreviated SI
5. SI Units
A system of standard measures that every
scientist uses
It consists of 7 base units which have real
measures in the real world
6. SI Units
Base
Quantity Base unit
Time second (s)
Length meter (m)
Mass kilogram (kg)
Temperature kelvin (K)
Amount of substance mole (mol)
Electric current ampere (A)
Luminous intensity candela (cd)
7. Time
Base unit for time is the second
It is based on the frequency of microwave
radiation given off by a cesium-133 atom
8. Length
The SI unit for length is
the meter (m).
The distance that light
travel through a vacuum
Equals 1/300,000,000 of
a second
About 39 inches
9. Mass
Base unit for mass is the
kilogram (kg)
You may see grams (g)
or milligrams (mg)
Defined by a platinum-
iridium cylinder stored
in a bell jar in France
About 2.2 pounds
10. Temperature
You classify an object as
hot or cold by whether
heat flows from you to the
object or from the object
to you.
Heat flows from hot to
cold.
Thermometers are used
to measure temp.
SI unit of temp is kelvin
(K)
11. Temperature
In science, the celsius and kelvin scales are most
often used.
To convert from celsius to kelvin: add 273
ex: -39º C + 273 = 234 K
To convert from kelvin to celsius: subtract 273
ex: 332 K – 273 = 59ºC
12. Der ived Unit s
Not all quantities can be
measured with base units
Volume—the space occupied by
an object
-measured in cubic meters
(cm3)
-or liters (L) or milliliters (ml)
13. Der ived Unit s
Density—a ratio that compares the mass of an
object to its volume
--units are grams per cubic centimeter (g/cm 3)
D = m Density equals
V mass divided by
volume.
14. Example: If a sample of aluminum has a
mass of 13.5g and a volume of 5.0 cm3,
what is its density?
Density = mass
volume D= 13.5 g
5.0 cm3
D = 2.7 g/cm3
15. Suppose a sample of aluminum is placed in a 25 ml
graduated cylinder containing 10.5 ml of water. A
piece of aluminum is placed in the cylinder and the
level of the water rises to 13.5 ml. The density of
aluminum is 2.7 g/cm3. What is the mass of the
aluminum sample?
17. Other Derived Quantities
• Velocity or speed- distance an obj travels over a
period of time
– V = ∆d/ t
– Units: m/s
• Force – push or a pull exerted on an object
– F = m*a m= mass a= acceleration
– Units: Kg * m/s2 = Newton (N)
18. Metric Prefixes
• To better describe the range of possible
measurements, scientists add prefixes to the base
units.
• For example: 3,000 m = 3 km (easier to manage)
• Most common prefixes:
– King Henry Died by Drinking Chocolate Milk
• Metric prefixes are based on the decimal system
19. Converting Between Units
• To convert b/w units simply move the decimal
place to the right or left depending on the
number of units jumped.
• Ex: K he da base d c m
– 24.56 m = 245.6 dm = 2,4560 mm
• May use power of 10 to multiply or divide
– Big units to small units Multiply
– Small units to big units divide
21. Scientific Notation
• A way to handle very large or very small
numbers
• Expresses numbers as a multiple of 10 factors
• Structure: a number between 1 and 10; and ten
raised to a power, or exponent
– Positive exponents, number is > 1
– Negative exponents, number is <1
Ex: 300,000,000,000 written in scientific
notation is 3.0 x 10 11
22. Change the following data into scientific notation.
a. The diameter of the sun is 1 392 000 km.
b. The density of the sun’s lower atmosphere is
0.000 000 028 g/cm3.
24. To add or subtract in scientific notation:
+ The exponents must be the same before doing the
arithmetic
+ Add/Subtract numbers, keep the power of 10.
Move the decimal to right
(make # bigger): subtract
from exponent (exp smaller)
Ex: To add the numbers
Move the decimal to left
2.70 x 107 (smaller #): add to exponent
(bigger exp)
15.5 x 106
0.165 x 108
26. To multiply or divide numbers in
scientific notation:
To multiply: multiply the numbers and
ADD the exponents
ex: (2 x 103) x (3 x 102)
2x3=6 3+2=5
Answer = 6 x 105
27. To multiply or divide numbers in
scientific notation:
To divide: divide the numbers and
SUBTRACT the exponents
ex: (9 x 108) ÷ (3 x 10-4)
9÷3=3 8 – (-4) = 12
Answer = 3 x 1012
29. Dimensional analysis
• A method of problem-solving that focuses on the
units used to describe matter
• Converts one unit to another using
conversion factors in a fraction format
– 1teaspoon = 5 mL 1 tsp or 5 ml
5 ml 1 tsp
– 1 km = 1000 m 1 km or 1000 m
1000 m 1 km
30. Dimensional analysis
cont….
• To use conversion factors simply write:
1. The number given with the unit
2. Write times and a line (x ______).
3. Place the unit you want to cancel on the bottom.
4. Use a conversion factor that contains that unit
5. Use as many conversion factors until you
reach your answer
Conversion factor
– ex: Convert 48 km to meters: 1km = 1000 m
48 km x 1000m
1km
= 48,000 m
34. You can convert more than one unit at a time:
What is a speed of 550 meters per second
in kilometers per minute?
HINTs:Convert one unit at a time!
Units MUST be ACROSS from each
other to cancel out!
36. Sometimes an estimate is acceptable and
sometimes it is not.
Okay?
When you are driving to the beach
Miles per gallon your car gets
Your final grade in Chemistry X
37. When scientists make measurements, they evaluate
the accuracy and precision of the measurements.
Accuracy—how close a measured value
is to an accepted value.
Not accurate Accurate
38. Precision—how close a series of
measurements are to each other
Not precise Precise
39. Density Data collected by 3 different students
Accepted density
of Sucrose = Student A Student B Student C
1.59 g/cm 3
Trial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3
Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3
Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3
Average 1.57 g/cm3 1.51 g/cm3 1.70 g/cm3
Which student is the most accurate? Which is most
precise? What could cause the differences in data?
40. It is important to calculate the difference
between an accepted value and an
experimental value.
To do this, you calculate the ERROR in
data. (experimental – accepted)
Percent error is the ratio of an error to
an accepted value
Percent error = error
x 100
accepted value
41. Calculate the percent error for
Student A
Percent error = error x 100
accepted value Density Accepted Error
Trial value (g/cm3)
(g/cm3)
First, you must 1 1.54 1.59
calculate the error!!
2 1.60 1.59
Error = (experimental – accepted) 3 1.57 1.59
43. Significant Figures
Scientists indicate the precision of
measurements by the number of digits they
report (digits that are DEPENDABLE)
Include all known digits and one estimated
digit.
A value of 3.52 g is more precise than a
value of 3.5 g
A reported chemistry test score of 93 is
more precise than a score of 90
44. Significant Figures
There are 2 different types of numbers
o Exact
o Measured
Exact numbers are infinitely important
o Counting numbers : 2 soccer balls or 4 pizzas
o Exact relationships, predefined values 1 foot = 12 inches , 1 m = 100 cm
Measured number = they are measured with a measuring device
(name all 4) so these numbers have ERROR.
When you use your calculator your answer can only be as
accurate as your worst measurement
45. Learning Check
Classify each of the following as an exact or a
measured number.
1 yard = 3 feet
The diameter of a red blood cell is 6 x 10-4 cm.
There are 6 hats on the shelf.
Gold melts at 1064°C.
45
46. Solution
Classify each of the following as an exact (1) or a
measured(2) number.
This is a defined relationship.
A measuring tool is used to determine length.
The number of hats is obtained by counting.
A measuring tool is required.
46
47. 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.
• This guess gives error in
47
data. Chapter Two
48. 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
•
48 The last digit an 7 was our guess...stop there
50. Measured Numbers
• Do you see why Measured Numbers have
error…you have to make that Guess!
• All but one of the significant figures are
known with certainty. The last significant
figure is only the best possible estimate.
• To indicate the precision of a measurement,
the value recorded should use all the digits
known with certainty.
50
51. Rules for significant figures
1. Non-zero numbers are always significant 72.3 g has__
2. Zeros between non-zero numbers are 60.5 g has__
significant
3. Leading zeros are NOT significant
0.0253 g has __
Leading zeros
4. Trailing zeros are significant after a 6.20 g has__
number with a decimal point Trailing zeros 100 g has__
52. Determine the number of significant figures in
the following masses:
a. 0.000 402 30 g
b. 405 000 kg
a. 0.000 402 30 g 5 sig figs
b. 405 000 kg 3 sig figs
53. To check, write the number in scientific
notation
Ex: 0.000 402 30 becomes
4.0230 x 10-4
and has 5 significant figures
55. Rounding to a specific # of sig figs
When rounding to a specific place using sig
figs, use the rounding rules you already
know. 1 2 3 4
ex: Round to 4 sig figs: 32.5432
1. Count to four
from left to right:
2. Look at the number
to the right of the 4th
digit and apply
32.54
rounding rules
57. Calculations and Sig Figs
• Adding/ Subtracting:
– Keep the least amount of sig fig in the decimal
portion only.
– Ex:
a. 0.011 + 2.0 =
b. 0.020 + 3 + 5.1 =
• Multiplying/ Dividing:
– Keep the least amount of sig figs total
– Ex:
a. 270/3.33 =
b. 2.3 x 100 =
58. Calculations and Sig Figs
• Follow your sig figs through the problem,
but round at the end
– Ex: (3.94 x 2.1) + 2.3418/ .004
