1. Measurement and Calculations

2. Qualitative Measurement –
Chemistry –
Qualitative Measurement –
Quantitative Measurement –
the science that deals with the materials of the universe and the changes these materials undergo
Qualities or observations that can be made about a substance ex: the substance is a yellow solid
a measurement that consists of a number and a unit
ex: the substance weighs 3.45 grams

3. Units
tells what scale or standard is being used to represent the measurement
International System (SI)
SI Base Units:
Length:
measures distance
Mass:
quantity of matter present in an sample
Volume:
1 mL = 1 cm3
three-dimensional space occupied by a sample
Temperature:
TK = T°C + 273
Time:
Pressure:
Energy/Heat:
Counting Atoms:
meter
grams
Liter, centimeter cubed, decimeter cubed
1 L = 1 dm3
Kelvin, Celsius
second
Pascals
Joules
moles

4. Units * * * * * Common metric prefixes (MEMORIZE)
Giga x 109 _ = 1 G_
Mega x 106 _ = 1 M_
Kilo _ = 1 k_
Hecto _ = 1 H_
Deka _ = 1 D_
(base) – meter, liter, gram…
deci- 1 _ = 10 d_
centi- 1 _ = 100 c_
milli- 1 _ = 1000 m_
micro- 1 _ = 1 x 106 _ ( = lowercase Greek Mu)
nano- 1 _ = 1 x 109 n_
pico- 1 _ = 1 x 1012 p_ * * * * *

5. Scientific Notation
Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10
If you move the decimal point-
left  positive exponent right  negative exponent
Ex: 200 g mL 2 1 1 2 3
2 x 102 g
3.14 x 10-3 mL

6. Converting from Scientific Notation to Ordinary Numbers
move the decimal point-
positive exponent  right negative exponent  left
Ex: x 101 cm x 10-3 m 1 3 2 1
63.2 cm m

7. Learning Check Try these: 657000000000 m 0.000000235 g 9.34 x 102 cL
3.35 x 10-3 L
6.57 x 1011 m
2.35 x 10-7 g
934 cL L

8. Limits to Measurements
When measuring you should always ______________ the _______ digit of your measurement
Your measurement should be recorded to ONE PLACE VALUE BEYOND the ______________marking
Your Estimate (or _____________ number) should be the final one on the right.
If the tool is digital, _________ the given number– no estimated number.
Measurements always
have some degree of
uncertainty (estimation)
estimate
last
calibration
uncertain
record

9. Ex 1: Measure the volume of liquid in the Graduated cylinder.
Remember: The volume is read at the bottom of the liquid curve (called the meniscus).
Ex 3: Measure the volume of liquid in the buret.
Ex 2: Measure the line using both rulers.
7.5 cm
42.8 mL
15.75 mL
7.56 cm

10. Learning check
Read the following pieces of equipment, record your answer with the estimated digit and units. 1. 4. 2. 5. 3.

11. Significant Figures All certain numbers plus first uncertain digit
Rules for counting Sig. Figs.
3578 =
4 SF
1. All nonzero numbers are significant.
236 =
3 SF
2. Zeros
a. Leading Zeros – precede all nonzero digits, they NEVER COUNT
.0025 =
2 SF
.0009 =
1 SF
b. Captive (Trapped) Zeros – fall between two nonzero digits, they ALWAYS COUNT =
3 SF
20502 =
5 SF
6008 =
4 SF
c. Trailing Zeros – come at the end of a number and count IF there is a DECIMAL POINT =
7 SF =
5 SF
3000. =
4 SF
3000 =
1 SF
3. Exact numbers – have infinite number of sig. figs., they arise from definitions
1 inch = 2.54 cm, 1 g = 1000 mg

12. Rounding If the digit to be removed is –
less than 5, the preceding digit stays the same
equal or greater than 5, increase the preceding digit by 1
When rounding off, use ONLY the first number to the right of the last significant figure
Ex: Round to 3 SF $ 10,079 g cm
1000. mL
= $10,100
= g
= cm
= x 103 mL

13. Learning Check
Determine the number of significant figures in the following numbers: g
9.00 mm mL
Round each number to 2 significant figures.

14. Calculations Notes

15. Uncertainty in Measurement
close
Accuracy: - How _________ a measurement is to the actual or _________value. To evaluate accuracy you must __________ the true value. For example, knowing a watch is 5 min fast…The time on the watch is ________ accurate and you know it is not accurate b/c you know the real time and can make an ________.
Shooting Free Throws - Accuracy can be measured by how many are __________.
accepted
know
not
adjustment
baskets

16. Precision: set actual value similar shots spot side right repeat
1st Meaning of Precision
How close a ____________ of measurements are to the _________________. To evaluate precision you must compare the values of 2 or more _______________ measurements.
Ex. Measure the temperature of water three times. Which set of measurements are more precise?
Thermometer 1: 22.3oC, 22.3oC, 22.4oC Thermometer 2: 24.5oC, 20.1oC, 18.7oC
Shooting Free Throws - Precision can be measured by how many _______ in the same _________. Ex. Consistently hitting the ___________ of the rim and missing. Not accurate b/c not making the shots, but precise b/c results are repeated.
Science – should be both accurate (___________) and precise (can ____________ it consistently)
set
actual value
similar
shots
spot
side
right
repeat

17. 2nd Meaning of Precision
Precision can also refer to how __________ a measurement is (more decimal __________ = more precise)
Consider mass of sugar in bubble gum
5 g - wide range of values that it could be! - Could be between 4.5 g and 5.4 g and rounded to 5 g.
5.0 g gives you more information – Could be between 4.95 g and 5.04 g.
5.00 g gives you even more information – Could be between g and g
More numbers to ______________ of decimal, more precise the measurement is!
precise
places
right

18. Learning Check
Think of an example, from your life, of accuracy and precision.

19. Multiplication and Division
Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate). LEAST NUMBER OF SIG FIGS!
Ex 1: m x 7.5 m Ex. 2: m2 / 2.1 m
4 sf
2 sf
3 sf
2 sf
34.725
35 m2
4.0 m

20. Addition and Subtraction
Align the decimal points and carry out the calculation. First column from the left with an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP) LEAST NUMBER of DECIMAL PLACES!
Ex 1: g g g Ex. 2: m m
6.341
.789
4.2
6.799
2.41
11.3 g
4.39 m
GAP
GAP
11.330
4.389

21. Learning Check
22.4 L x 9.3 L
g g

22. Scientific Notation and Multiplication and Division
Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F.
Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F.
Ex 1: (1.00 x 103 m)(3.2 x 102 m) Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3)
3.2 x 105 m2
3.0 x 102 g/cm3

23. Scientific Notation and Addition and Subtraction
must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent
Ex 1: 3.0 x 1023 m x 1022 m 1
3.0 x 1023 m x 1023 m
3.0
.10
3.1 x 1023 m
GAP
3.10

24. Learning Check
x 105 g x 104 g
x 1023 m ÷ 1.7 x m

25. Problem Solving and Dimensional Analysis
Conversion factor – ratio of two parts of the statement that relates the two units
Equivalence Statement – true statement in fraction form
Dimensional Analysis – when used properly all units will cancel out except the desired unit
2.54 cm = 1 inch
100 cm = 1 m
2.54 cm
1 inch
1 inch
2.54 cm
100 cm
1 m
1 m
100 cm or or
Wanted UNIT
Desired UNIT # #
Given with UNITS
x ________________
x ______________ = #
Given UNIT #
Wanted UNIT

26. Ex. 1: 250 m = ___________ km Ex. 2: 3.54 g = ___________ mg
1 km = 1000 m
Ex. 1: 250 m = ___________ km
Ex. 2: g = ___________ mg
Ex. 3: kg = __________ mg
250 m 1 km
x ___________
.25 km =
1000 m
1 g = 1000 mg
1000 mg
3.54 g
x ___________
3540 mg =
1 kg = 1000 g 1 g
0.542 kg
1000 g
1000 mg
x ________
x __________ = mg 1 kg 1 g
1 g = 1000 mg

27. Learning Check
mm = __________ km
g = __________ µg

28. Determining Error accepted experimental absolute
___________________value - correct value based on reliable references
___________________value - value measured in the lab
Error = experimental value – accepted value (Note: error can be positive or negative) You will take the ___________ value of this when you calculate percent error.
experimental
absolute

29. Determining Percent (%) Error
Percent error = absolute value of error divided by accepted value and multiplied by 100%
% error = (experimental value – accepted value) x 100%
accepted value
Example: You take three temperature readings of a beaker of boiling water and record: 91.3oC, 90.9oC, and 91.1oC. Evaluate accuracy, precision, and error.
Accurate?
No, water boils at 100oC
Precise?
Yes, values are close to each other
Error
Find average experimental data
Use formula
(91.3oC oC oC)/3 =
91.1oC
% error = (91.1 oC – 100 oC) x 100%
100 oC
= %

30. Learning Check
1. At a track meet, you time a friend running 100 m in seconds. The officials time her at seconds. What is your percentage error?

31. For Fun!
Hagrid instructed Harry to give the delivery owl five Knuts for a newspaper (p. 62). A weekday newspaper costs $0.25. At Gringots, Harry learned that there are seventeen Sickles to a Galleon and twenty-nine Knuts to a Sickle (p. 75). Harry then paid seven Galleons for his new wand-Holly and phoenix feather (p. 85). Use dimensional analysis to calculate how much Harry’s wand would cost in dollars?
On the train, Harry paid eleven Sickles and seven Knuts for junk food from the snack trolley. How much money did he spend?
7 Galleons 17
Sickles 29
Knuts
.25
dollars
$172.55
x ___________
x ___________
x ______________ = 1
Galleon 1
Sickles 5
Knuts 29
Knuts
.25
dollars
$ 15.95
11 Sickles
x __________
x ___________ = 1
Sickle 5
Knuts
$16.30
7 Knuts
x ___________
.25
dollars =
$ 0.35 5
Knuts