1. Measurement The Metric System and SI Units Converting Units
Uncertainty in Measurement
Significant Figures
Measuring Volume and Mass
Density
Measuring Temperature and Time

2. SI Units
Many different systems for measuring the world around us have developed over the years.
People in the U.S. rely on the English System.
Scientists make use of SI units so that we all are speaking the same measurement language.

3. Data, results and units Data Measurements and observations. Results
Data obtained from an experiment.
May be converted using known equations.
Units
Defines the quantities being measured.
All measurements must have units.
To communicate our results, we must use standard units

4. Units are important 45 000 has little meaning, just a number
$45,000 has some meaning - money
$45,000/yr more meaning - person’s salary

5. Measurements in chemistry
English units.
- Still commonly used in the United States.
Weight ounce, pound, ton
Length inch, foot, yard, mile
Volume cup, pint, quart, gallon
Not often used in scientific work
- Very confusing and difficult to keep
track of the conversions needed.

6. Measurement in chemistry
English units. Vary in size so you must memorize many conversion factors.
Common English measures of volume
1 tablespoon = 3 teaspoons
1 cup = tablespoons
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 peck = 2 gallons
1 bushel = pecks

7. Example How many teaspoons in a barrel of oil?
1 barrel of oil = 42 gallons
1 gallon = 4 quarts
1 quart = 4 cups
1 cup = 16 tablespoons
1 tablespoon = teaspoons
1 bbl x x x x x 3
gal
bbl qt
gal
cup qt
tbl
cup
tsp
tbl
= tsp

8. Measurement in chemistry
Metric Units One base unit for each type of measurement. Use a prefix to change the size of unit.
Some common base units.
Type Name Symbol
Mass gram g
Length meter m
Volume liter L
Time second s
Energy joule J

9. Metric prefixes Changing the prefix alters the size of a unit.
Prefix Symbol Factor
mega M
kilo k
hecto h
deka da
base
deci d
centi c
milli m

10. SI units SI - System International
Systematic subset of the metric system.
Only uses certain metric units.
Mass kilograms
Length meters
Time seconds
Temperature kelvin
Amount mole
Other SI units are derived from SI base units.

11. Example. Metric conversion
How many milligrams are in a kilogram?
1 kg = 1000 g
1 g = 1000 mg
1 kg x x 1000
= mg kg g mg g

12. Converting units Factor label method
Regardless of conversion, keeping track of units makes things come out right
Must use conversion factors
- The relationship between two units
Canceling out units is a way of checking that your calculation is set up right!

13. Common conversion factors
English Factor
1 gallon = quarts qt/gal
1 mile = 5280 feet 5280 ft/mile
1 ton = 2000 pounds 2000 lb/ton
Common English to Metric conversions
Factor
1 liter = quarts qt/L
1 kilogram = 2.2 pounds 2.2 lb/kg
1 meter = yards yd/m
1 inch = 2.54 cm cm/inch

14. Example
A nerve impulse in the body can travel as fast as 400 feet/second.
What is its speed in meters/min ?
Conversions Needed
1 meter = feet
1 minute = seconds

15. ....Fast Example m 400 ft 1 m 60 sec min 1 sec 3.3 ft 1 min ? = x x
7273

16. Uncertainty in Measurement
All measurements contain some uncertainty.
We make errors
Tools have limits
Uncertainty is measured with
Accuracy How close to the true value
Precision How close to each other

17. Accuracy How close our values agree with the true value. Here the
average value
would give a
good number
but the numbers
don’t agree.
Large random error

18. Precision How well our values agree with each other. Here the numbers
are close together
so we have good
precision.
Poor accuracy.
Large systematic
error.

19. Accuracy and precision
Our goal!
Good precision
and accuracy.
These are
values we
can trust.

20. Accuracy and precision
Predict the effect on accuracy and precision.
Instrument not ‘zeroed’ properly
Reagents made at wrong concentration
Temperature in room varies ‘wildly’
Person running test is not properly trained

21. Significant figures Method used to express accuracy and precision.
You can’t report numbers better than the method used to measure them.
67.2 units = three significant figures
Certain
Digits
Uncertain
Digit

22. Significant figures
The number of significant digits is independent of the decimal point.
255
25.5
2.55
0.255
0.0255
These numbers
All have three
significant figures!

23. Significant figures: Rules for zeros
Leading zeros are not significant.
three significant figures
Leading zero
Captive zeros are significant.
four significant figures
Captive zero
Trailing zeros are significant.
five significant figures
Trailing zero

24. Significant figures Zeros are what will give you a headache!
They are used/misused all of the time.
Example
The press might report that the federal deficit is three trillion dollars. What did they mean?
$3 x 1012 or
$3,000,000,000,000.00

25. Significant figures
In science, all of our numbers are either measured or exact.
Exact - Infinite number of significant figures.
Measured - the tool used will tell you the level of significance. Varies based on the tool.
Example
Ruler with lines at 1/16” intervals.
A balance might be able to measure to the nearest 0.1 grams.

26. 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 the proper number of significant figures.
= x 10-3
Three Significant
Figures

27. Scientific notation If a number is larger than 1
The original decimal point is moved X places to the left.
The resulting number is multiplied by 10X.
The exponent is the number of places you moved the decimal point.
= x 108

28. Scientific notation If a number is smaller than 1
The original decimal point is moved X places to the right.
The resulting number is multiplied by 10-X.
The exponent is the number of places you moved the decimal point.
= x 10-7

29. Scientific notation
Most calculators use scientific notation when the numbers get very large or small.
How scientific notation is displayed can vary.
It may use x10n
or may be displayed
using an E.
They usually have an Exp or EE
This is to enter in the exponent.
E-2

30. Examples
3.78 x 10 5
8931.5
x 10 3
5.93 x
4 x

31. 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

32. Significant figures and calculations
Addition and subtraction
Report your answer with 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

33. Significant figures and calculations
Multiplication and division.
Report your answer with the same number of digits as the quantity have the smallest number of significant figures.
Example. Density of a rectangular solid.
25.12 kg / [ (18.5 m) ( m) (2.1m) ]
= 2.8 kg / m3
(2.1 m - only has two significant figures)

34. Example 257 mg \__ 3 significant figures 120 miles 0.002 30 kg
23, $/yr
\__ 7 significant figures

35. 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.

36. 1st insignificant digit
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

37. Measuring volume Volume - the amount of space that an object occupies.
The base metric unit is the liter (L).
The common unit used in the lab is the milliliter (mL).
One milliliter is exactly equal to one cm3.
The derived SI unit for volume is the m3 which is too large for convenient use.

38. Measuring mass Mass - the quantity of matter in an object.
Weight - the effect of gravity on an object.
Since the Earth’s gravity is relatively constant, we can interconvert between weight and mass.
The SI unit of mass is the kilogram (kg). However, in the lab, the gram (g) is more commonly used.

39. Density What is the density of 5.00 mL of a fluid if it
has a mass of 5.23 grams?
d = mass / volume
d = g / 5.00 mL
d = g / mL
What would be the mass of 1.00 liters of this
sample?

40. Example. Density calculation
What would be the mass of 1.00 liters of the fluid sample?
The density was 1.05 g/mL.
density = mass / volume
so mass = volume x density
mass = 1.00 L x x 1.05
= 1.05 x 103 g ml L g mL

41. Temperature conversion
Temperature - measure of heat energy.
Three common scales used
Fahrenheit, Celsius and Kelvin.
9oF
5oC
oF = 32oF + (oC) X
oC = (oF - 32oF)
K = (oC + 273) X
5oC
9oF
SI unit
1 K
1oC

42. Measuring time The SI unit is the second (s).
For longer time periods, we can use SI prefixes or units such as minutes (min), hours (h), days (day) and years.
Months are never used - they vary in size.