1. Chemistry Mathematics
Measurement
3221.MATH.1; 3221.MATH.2

2. Learning Goals
Write the names and abbreviations for the units used in measurements of length, volume, and mass
Label measurements as accurate or precise
Write a number in scientific notation
Determine the number of significant figures in measured numbers
Adjust calculated answers to the correct number of significant figures.
Use numerical prefixes to do metric conversions through decimal placement.

3. Units of Measurement 2 parts to any measurement: number and unit
Units are extremely important in reporting and working with scientific numbers and they must be included
The number of digits in a measurement reflects a degree of precision: the more digits in the measurement, the more precise it is; fewer digits, less precision
Why is this important??
Why must both parts of a measurement be included in order to be determined as correct??

4. The units make all the difference!!!
Read the following:
When my son was 7 he walked 3, and when he was 4 he threw his baseball 8 and said his school was 5 away.
When my son was 7 months old he walked 3 steps, and when he was 4 years old he threw his ball 8 feet and said his school was 5 minutes away.
The units make all the difference!!!

5. Uncertainty in Measurement
Accuracy: how close a measurement is to the accepted value
Precision: degree of “agreement” between several measurements of the same quantity
A MEASUREMENT CAN ONLY BE AS PRECISE AS THE INSTRUMENT USED!!!
How many divisions are on the ruler? How precise is the ruler? What is the most precise a measurement can be using this ruler? (answer: 2 decimal places—why??)

6. Accuracy and Precision Illustration
What makes something accurate? Precise?

7. Two major systems: English system -used only in the United States
-inches, yards, pounds
2. Metric system
-International System (SI system) is the system of measurement for the scientific world
-centimeters, meters, kilograms

8. Fundamental SI Units Quantity Symbol Unit name Unit abbreviation
Length l
Meter m
Mass
Kilogram kg
Time t
Second s
Temperature T
Kelvin K
Amount of substance n
Mole
mol
Electric current I
Ampere A
Luminous intensity Iv
Candela cd

9. What do the units mean?
Unit: predefined standard of measurement or basis of comparison
Second: 60 s = 1 min
1 meter is slightly longer than 1 yard a 100 yd football field is only 91.4 m
1 kg = lb
Remember: mass is different than weight, which is affected by gravity

10. Prefixes in SI system Prefix Symbol Meaning Exponential Notation mega-
1,000,000
106
kilo- k
1,000
103
hecto- h
100
102
deka- da 10
101
------
----- 1
deci- d
0.1
10-1
centi- c
0.01
10-2
milli- m
0.001
10-3
micro-
10-6
nano- n
10-9
What are mnemonics? Does anyone know a mnemonic for the SI prefixes? Mighty King Hector Died---Driving crazy mini-motorcycles nightly.

11. Prefix Multipliers
Used with the standard units of the SI system, rather than having different “units” with which to make comparisons
Multipliers change the value of the unit by powers of 10
Prefix multipliers allow us to express a wide range of measurements in units that are similar in size to the quantity we are measuring
Choose the prefix that is most convenient for a particular measurement

12. Volume/ amt of substance
Derived SI Units
Quantity
Symbol
Unit name
Abbreviation
Derivation
Area A
Square meter m2
Length x width
Volume V
Cubic meter m3
Length x width x height
Density D
kg/ m3
Mass/volume
Molar mass M
kg/ mol
Mass/amt of substance
Molar volume Vm
m3/ mol
Volume/ amt of substance
Energy E
Joule J
Force x length
What is the definition of volume? Area?
ANY UNIT OF LENGTH, WHEN CUBED (RAISED TO THE THIRD POWER), BECOMES A UNIT OF VOLUME
1 cm3 = 1 mL 1 dm3 = 1 L

13. Uncertainty in Measurements
Measured numbers: numbers you obtain when you use a measuring tool to determine your height, weight, or temperature
To report a measurement, first read the numerical value of the marked line. Finally, estimate between the smallest marked lines.
When an estimate ends on a marked line, a zero is written for the estimated digit.

14. Significant Figures
Scientific numbers are recorded so that every digit is certain except for last, which is estimated.
48.872
When recording measurements, only estimate ONE digit beyond the smallest division on the instrument being used!!

15. Reading Volume
Meniscus: the curved portion at the top of a volume of liquid
Most liquids have a concave meniscus, however mercury has a convex meniscus

17. Rules for determining significant figures:
All nonzero digits are significant
2. Interior zeros (zeros between 2 numbers) are significant
3. Trailing zeros (zeros after a decimal point) are significant
4. Leading zeros ( zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point.

18. Practice Problems
2.0012
0.001
4.100
0.1000
100.25

19. Solutions to Problems 0.00789 3 significant figures (0.00789)
(2.0012)
(0.001)
(4.100)
(0.1000)
( )
(100.25)

20. Exact numbers
Exact numbers have an unlimited number of significant figures
3 sources
1. accurate counting of discrete objects
3 atoms means atoms
2. defined quantities
100 cm = 1 m means cm =1.00m
3. integral numbers that are part of an equation
radius = diameter/ 2

21. Significant Figures in Calculations
In multiplication or division, the result carries the same number of significant figures as the factor with the fewest significant figures
In addition or subtraction, the result carries the same number of decimal places as the quantity carrying the fewest decimal places

22. Scientific Notation
Used to write cumbersome numbers in a compact manner
1.2 x 10-10 exponent (n)
Decimal part exponential part
To convert a number to scientific notation:
1. move the decimal point to obtain a number between 1 and 10.
2. multiply by 10 raised to the number of places you moved the decimal point
-if decimal moved left: positive exponent
-if decimal moved right: negative exponent

23. Practice

24. Percent Error NO MEASURED VALUE WILL EVER BE EXACT!!
The percentage by which a measurement deviates from the accepted value
NO MEASURED VALUE WILL EVER BE EXACT!!
% Error = Accepted Answer - Experimental Answer x 100
Accepted Answer
WORK EXAMPLE PROBLEMS!!!

25. Practice Problems
1. Samantha S. Sloppiness measured the volume of her soda before she drank it for her midmorning snack. She measured the volume of the 12 oz. bottle to be 14 oz.
2. Clyde Clumsy was directed to weigh a 500 g mass on the balance. After diligently goofing off for ten minutes, he quickly weighed the object and reported 458 g.
3. Pretty Patty Pestilence had casually recorded her grades for the nine weeks in her notebook. She concluded she had 250 points out of 300 for the grading period. However, Miraculous (chemistry teacher) determined she had 225 points out of 300 and awarded her a "C" for the grading period.
4. Drew D. Ditzy came to Miraculous with a problem. Drew was told to measure 50 cm of copper wire to use in an experiment. Since his ruler only measured to 45 cm he used this amount of wire and his experiment was a failure.
5. Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55 mph not 65 mph.