1. Measurement Measurement Systems Accuracy vs. Precision Percent Error
Significant Digits
Scientific Notation
Dimensional Analysis

2. Measurements Involve Quantities
Quantity = number + unit
UNITS DO MATTER!!
If you are going “100” could you get a ticket?
What does it depend upon?

3. SI Units are Universally Accepted
Measure
Symbol
Base Unit
Abbrev.
Length l
meter m
Mass m
kilogram kg
Time t
second s
Temp T
kelvin K
Amount n
mole
mol

4. To do this, we must know some equivalents. These are called
CONVERSION FACTORS In the real world, it is necessary to convert from one unit to another.
To do this, we must know some equivalents. These are called
“conversion factors!”
A conversion factor expresses an equal value for a measurement but in different units.
Example: 12 inches = 1 foot

5. Metric System Conversion Factors
1012 meters = 1 terameter (Tm)
109 meters = 1 gigometer (Gm)
106 meters = 1 megameter (Mm)
103 meters = 1 kilometer (km)
102 meters = 1 hectometer (hm)
10 meters = 1 dekameter (dam)
1 meter = 10 decimeters (dm)
1 meter = 102 centimeters (cm)
1 meter = 103 millimeters (mm)
1 meter = 106 micrometers (mm)
1 meter = 109 nanometers (nm)
1 meter = 1012 picometers (pm)
EASY – ALWAYS BASED ON A FACTOR OF TEN!!!!!!!! D I S T A N C E

6. Metric System Conversion Factors
1012 grams = 1 teragram (Tg)
109 grams = 1 gigogram(Gg)
106 grams = 1 megagram (Mg)
103 grams = 1 kilogram (kg)
102 grams = 1 hectogram (hg)
10 grams = 1 dekagram (dag)
1 gram= 10 decigrams (dg)
1 gram= 102 centigrams (cg)
1 gram = 103 milligrams (mg)
1 gram = 106 micrograms (mg)
1 gram = 109 nanograms (ng)
1 gram = 1012 picograms (pg)
EASY – ALWAYS BASED ON A
FACTOR OF TEN!!!!!!!! MA S

7. Metric System Conversion Factors
1012 liters = 1 teraliter (Tl)
109 liters = 1 gigoliter (Gl)
106 liters = 1 megaliter (Ml)
103 liters = 1 kiloliter (kl)
102 liters = 1 hectoliter (hl)
10 liters = 1 dekaliter (dal)
1 liter = 10 deciliters (dl)
1 liter = 102 centiliters (cl)
1 liter = 103 milliliters (ml)
1 liter = 106 microliters (ml)
1 liter = 109 nanoliters (nl)
1 liter = 1012 picoliters (pl)
EASY – ALWAYS BASED ON A FACTOR OF TEN!!!!!!!! VO L
UME

8. METRICS – EASY!!! BASED ON MULTIPLES OF TEN!!!!!!
KNOW THE PREFIXES AND YOU KNOW THE POWER!!
WHY HAVEN’T AMERICANS SWITCHED???????
WHO KNOWS???? – WE HAVE BEEN TALKING
ABOUT IT FOR ABOUT FOUR DECADES, SINCE
I WAS A KID!!!
SO THAT WE CAN KEEP OUR SYSTEM AND USE
THE ONE THE REST OF THE WORLD USES,
WE MUST ALSO KNOW METRIC – ENGLISH CONVERSIONS!!!!!

9. English to Metric Conversion Factors
LENGTH: 1 inch = 2.54 centimeters 1 meter = inches 1 mile = kilometers MASS: 1 ounce = grams 1 pound = grams 1 kilogram = pounds 1 gram = grains VOLUME: 1 quart = liters 1 gallon = liters 1 liter = fluid ounces 1 fluid ounce = milliliters 1 liter = quarts NOT ALWAYS EASY – NOT A FACTOR OF TEN, not as precise!!!

10. SIGNS OF A GOOD MEASUREMENT:
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT

11. ACCURACY VS. PRECISION

12. Percent Error: A SIGN OF ACCURACY
Indicates accuracy of a measurement, how close you come to an accepted value
your value
accepted value

13. Percent Error Sample Calculation
Problem: A student determines the density of a substance to be g/mL. Find the % error if the accepted value of the density is g/mL.
% error = 2.9 %

14. Significant Figures: A Sign of Precision
Indicate precision of a measurement.
When making scientific measurements, you are allowed to estimate only one digit – THE LAST DIGIT!!!!!!!! All others you must know for certain!
2.35 cm

15. Examples of Scientific Measurements
ONLY ONE ESTIMATED DIGIT!!!!!

16. Examples of Scientific Measurements
AGAIN - ONLY ONE ESTIMATED DIGIT!!!!!

17. RULES FOR MEASURING: REPORT ALL OF THE DIGITS KNOWN FOR CERTAIN
ESTIMATE ONE DIGIT, THE LAST DIGIT
GIVE THE NUMBERS A LABEL

18. Rules for Estimating IF EACH LINE ON THE INSTRUMENT EQUALS
10, YOU CAN ESTIMATE TO THE 1
1, YOU CAN ESTIMATE TO THE 0.1
0.1, YOU CAN ESTIMATE TO THE 0.01
0.01, YOU CAN ESTIMATE TO THE 0.001

19. Make the Measurement BOTH ARE CORRECT!!!!! FOR THIS VOLUME:
2.7 IS KNOWN FOR CERTAIN,
NOW ESTIMATE THE NEXT DIGIT,
MAYBE 2.76 ml
MAYBE 2.77 ml
BOTH ARE CORRECT!!!!!

20. Significant Figures: How do we know what digits are significant when looking at a quantity?
Count all digits EXCEPT:
Leading zeros
Trailing zeros without a decimal point -- 2,500

21. Counting Sig Fig Examples
4 sig figs
3 sig figs
3. 5,280
3. 5,280
3 sig figs
5 sig figs

22. Adding and Subtracting Sig Figs
The rule is:
The answer must be rounded to the place value of the least precise measurement.
Example:
21.5 ml ml = 23.5 ml
This answer can only have one digit after the decimal point!!!

23. Multiplying and Dividing Sig Figs
The rule is:
The answer must have no more significant figures than there are in the measurement with the fewest number of significant figures.
Example:
15.82 mL x 2.4 g/mL = 38 g
This answer can only have 2 sig figs.

24. Practice Problems: 66.87 = 66.9 one digit after the decimal
= – = 23.6 x = 23,200 x = (2.315 – 1.72) x =
66.87 = 66.9 one digit after the decimal
1.045 = 1.05 two digits after the decimal
= 790. three sig figs
771,748 = 772,000 three sig figs
0.60 x = 7.3 two sig figs

25. Scientific Notation: Needed for very large and very small quantities
65,000 kg  6.5 × 104 kg
Converting into Scientific Notation:
Move decimal until there’s one nonzero digit to its left. Places moved = exponent.
Large # (>1)  positive exponent Small # (<1)  negative exponent
Only include sig figs.

26. Scientific Notation Practice Problems 2,400,000 g 0.00256 kg
7  10-5 km
6.2  104 mm
2.4 x 106 g
2.56 x 10-3 kg km
62,000 mm

27. Scientific Notation Using the calculator:
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
The answer must have two sig figs!!! Multiplication rules!
Type on your calculator:
EXP EE
EXP EE
ENTER
EXE
5.44 7
8.1 ÷ 4 =
= 670 g/mol
= 6.7 × 102 g/mol

28. The Process of Dimensional Analysis
Identify the known quantity and the unknown quantity.
Find equivalents or conversion factors which will act as ratios to find the unknown unit or units.
Decide on a pathway to solve the problem.
Set up the dimensional analysis grid.
Cancel out units appearing on both the top and bottom, leaving only the unit(s) for the answer.
Multiply the numbers on the top, divide by every number on the bottom.
Report the answer to the proper number of sig figs with the desired label.

29. Let’s try these! Convert the following: 3.53 yards to centimeters
0.25 miles to inches
4.333 gallons to milliliters
2.5 tons to kilograms
4500 milligrams to ounces
3,345 feet to kilometers
3.2 X 106 meters to feet
8.520 X 108 micrograms to pounds

30. Combinations of base units are called derived units.
Volume (m3 or cm3) = length x length x length
Area (m2 or cm2) = length x length
Density kg/m3 or g/cm3 = mass/volume

31. Derived Units
Follow the same protocol in conversion problems with the following twists:
If the known quantity is squared or cubed, the conversion factors must be squared or cubed as well.
If the known quantity is a ratio like m/s or kg/l or oz/cm, the denominator unit is now placed in the bottom of the first part of the dimensional analysis grid.
To convert the bottom unit, the conversion factors are now flipped to cancel from bottom to top.

32. Try these! Convert the following: 21.3 ft2 to yd2 345 in3 to cm3
1,234 g/cm3 to lb/liter
4.355 m/s to km/hr
23.4 mg/cm to lb/inch
4.2 X 109 picograms/microliter to lb/gallon
3.22 X 1012 ml/s to gallon/hr
6.5 X 10-7 g/cm2 to ton/mile2

33. IRREGULAR SHAPED OBJECT
Density Determination A. Must measure Mass, Volume, and Possibly Length
Mass -- Instrument? __________ Unit? ___________
Length -- Instrument? _________ Unit? ___________
Volume
OBJECT
METHOD
MEASURING INSTRUMENT
LIQUID
BLOCK OF WOOD
IRREGULAR SHAPED OBJECT

34. D. Density Calculations
Problem: An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass in milligrams.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ? mg
WORK:

35. E. More Density Calculations
Problem: A liquid has a density of 0.87 g/mL. What volume in liters is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ? L
M = 25 g
WORK:

36. C. Density by Graphical Analysis
Mass (g)
Volume (cm3)