Lap 3 Chapter 3
Scientific Measurement
Essential Question:
How do measurements affect how scientists study matter in the world around us?
3.1 Measurements and Uncertainty
A. Using and Writing Measurements
1. Measurement: quantity with number and unit
Important to scientific experiments
Ex:
Mars planet orbiter crashed because of wrong units
Calcium Carbide demo: 5 extra grams prevents top from popping
Insulin for diabetics needs to be measured exactly
Recipes rely upon measured ingredients
2. Scientists Use International System of Measurements (SI Units)
3. Scientific notation
Way to write a very large or tiny number
Number is written as product of 2 numbers - Coefficient and a number raised to power of 10
Example: 6.02 x 1023
602000000000000000000000 = number of atoms in 1 gram of H
Example: 3.27 x 1022
0.000000000000000000000327 grams = mass of 1 atom of Au
Examples of Scientific Notation
5.5 x 105
Power of +5: move 5 spots to the right (make larger)
5.5
5 5 0 0 0 0 . = 550000
7.8 x 10-3
Power of -3: move 3 spots to the left (make smaller)
7.8
0 . 0 0 7 8 = 0.0078
B. Accuracy and Precision
Measurements should be both correct and reproducible.
Accuracy: how close your measurement is to the actual value
Must compare one measured value to true value
Precision: how close a set of measurements are to each other
Compare two or more repeated measurements
Example: Given these sets of data:
A. 80o C, 79o C, 82o C
B. 77o C, 65o C, 73o C
C. 76o C, 76o C, 75o C
Which is the most precise?
C: all within 1 degree
Which is the most accurate if the liquid's known boiling point is 81o C?
A: average is closest to known value
C. Determining Error
Error: absolute value of the difference between the accepted or known value and the experimental value
Error = experimental value - accepted value
Percent error = Experimental value – Accepted value
100%
Known value
Example: You conduct an experiment and find the boiling point of water to be 98oC. What is percent error?
Experimental value = 98℃
Accepted value for boiling point of water =100℃
Solve:
l 98℃ - 100℃ l
100%
100℃
= .02 x 100% = 2%
D. Determining Significant Figures (Sig figs)
Different tools measure with different certainty
Significant figures tell how "good" your tool is
Def: measurement that includes all of the known digits plus one estimated digit
Must always record in correct significant digits or figures to indicate how precise the measurement was
Example: Ruler marked in meter will give a measurement with less significant figures than a ruler marked with
centimeters
E. Rules for significant figures
1. Every nonzero number is significant.
56 m = 2 sig figs
45978 mm = 5 sig figs
2. Zeroes between nonzero digits are significant.
305 K= 3 sig figs
230098 L = 6 sig figs
3. Final zeroes after a decimal point are significant.
6.70 mg = 3 sig figs
11.00 km = 4 sig figs
4. Final or trailing zeros without a decimal point are NOT significant.
900 g = 1 sig fig
150 ms = 2 sig figs
70000 g = 1 sig fig
5. Leftmost or leading zeros appearing in front of nonzero digits are NOT significant.
0.008 g = 1 sig fig
0.78 ms = 2 sig figs
0.00000006 cm = 1 sig fig
6. These rules do not apply to:
counting numbers
12 people (there can't be 12.3 people)
unlimited number of sig figs: 12.00000000..... people to infinity
conversion factors
1 m = 100 cm (these are exactly defined quantities, not measured)
Examples:
123 m
3 sig figs
Reason: 3 nonzero
9.800 x 105 s
4 sig figs
Reason: 2 nonzero + 2 final zeroes after decimal
(ignore 105 power: is never included in sig figs)
0.0708 g
3 sig figs
Reason: 2 nonzero + 1 zero between nonzero
F. Rules for significant figures in Calculations
A calculated answer cannot be more precise than the least precise measurement from which it was
calculated.
Calculated answer must be rounded to the correct number of sig figs
Rounding rules:
If the last insignificant number is 4 or less, round down
Example: 4.52 rounds to 4.5
Example: 0.0081 rounds to 0.008
If the last insignificant number is 5 or more, round up
Example: 4.56 rounds to 4.6
Example: 0.0087 rounds to 0.009
Sample Problem
Round off 314.721 meters to four significant figures and write the answer in scientific notation.
314.721 m = 314.7 m = 3.147 x 102
Rule for addition and subtraction:
Answer should be rounded to the same number of decimal places as the least number of decimal places
Example:
12.5 m + 4.35 m + 1.005 m
Find the number with the least number of decimal places after the decimal point
12.5 has only 1 place after the decimal point, this is the least
Answer should be rounded to 1 place after the decimal point
Answer on calculator 17.855 m
Answer should be rounded to 17.9 m
Another example:
51.78 cm + 2.000 cm + 13.00008 cm
51.78 has least number of places after decimal point: 2
Answer will be rounded to 2 places after decimal point
Answer on calculator 66.78008 cm
Answer rounded is 66.78 cm
Rule for multiplication and division
Answer should be rounded to same number of sig figs as the least number of sig figs
Example:
78.9 mm x 100 mm =
78.9 mm is 3 sig figs and 100 mm is 1 sig fig
Answer should be round to only 1 sig fig
Answer on calculator 78900 mm
Answer rounded to 80000 mm
Another example:
2.10 km X 0.70 km =
2.10 has 3 sig figs and 0.70 has 2 sig figs
Answer should be rounded to 2 sig figs
Answer on calculator: 1.47
Answer rounded to 1.5 km
How many sig figs in:
45.79 cm
300 km
0.04 mm
10.042 nm
15,000 km
34100 mL
0.000902 mL
6.02 x 1023
1.7 x 10-3
3.00 x 10-24
How many sig figs in the answer to this problem?
1.2 g x 3.45 g
1200 g ÷ 7.43 g
10.0 + 2.00
75.4523 - 3.231
(5.6 x 103) x (3.21 x 105)
(7.932 x 104) + (2.3 x 104)
3.1 Section Assessment
1. How are accuracy and precision evaluated?
2. How does the precision of a calculated answer compare to the precision of the measurements used to obtain
it?
3. A technician experimentally determined the boiling point of octane to be 124.1 0C. The actual boiling point of
octane is 125.7 0C. Calculate the error and the percent error.
4. Determine the number of significant figures in each of the following:
a. 11 soccer players
b. 0.070020 meter
c. 10,800 meters
d. 5.00 cubic meters
5. Solve the following and express each answer in scientific notation and to the correct number of significant
figures.
a. (5.3 x 104) + (1.3 x 104)
b. (7.2 x 10-4)
(1.8 x 103)
c. 104 x 10-3 x 106
d. (9.12 x 10-1) - (4.7 x 10-2)
e. (5.4 x 104) x (3.5 x 109)
3.2 SI Units (Le Systeme International d'Unites)
A. Common SI units in Chemistry
Length
Mass
Temperature
Time
Amount of substance
Metric prefixes for large or small units – most commonly used:
Prefix
Meaning
1,000 times larger than the unit it precedes
100 times smaller than the unit it precedes
1,000 times smaller than the unit it precedes
B. Units of Length
Meter is base unit
1 kilometer = 1000 m
100 cm = 1 m
1000 mm = 1 m
1 meter = height of doorknob from the floor
1 kilometer = length of about five city blocks
1 centimeter = width of a shirt button
1 millimeter = thickness of a dime
C. Units of Volume
Volume = amount of space occupied by a sample of matter
Found by length x width x height
SI unit is m3
Liter is more commonly used
1 L = 1000 cm3
1 mL = 1 cm3
liter = quart of milk
milliliter = 20 drops of water
cubic centimeter = cube of sugar
D. Units of Mass
Mass = quantity of matter
Kilogram is standard mass unit
Previously based on mass of 1 liter of H2O
Now based on mass of cylinder of platinum and irridium
1000 g = 1kg
Factor
1000 mg = 1 g
Weight is force of gravity on an object’s mass
Weight can vary by location, but mass is constant (on the moon 1/6 of weight)
E. Units of Temperature
Temperature = measure of how hot or cold object is
Object's temp determines direction of heat transfer
Hold a glass of hot water - heat transfers to your hand
Hold an ice cube - heat transfers from hand to ice cube
Almost all substances expand when temp increases and contract when temp decreases, except water
Celsius scale: set at 0 degrees C for freezing water and 100 degrees C for boiling water
Kelvin or absolute scale:
Does not use degrees
freezing point of water is 273.15 K
boiling point of water is 373.15 K
0 K is called absolute zero
Lowest possible temperature; nothing could be colder and no heat energy remains
K = C +273
C = K -273
Example of conversion
5 K = _____ degrees C
5 K - 273 = -268 degrees C
F. Units of Energy
Energy = capacity to do work or produce heat
SI unit for energy is Joule (J)
Also use calorie (cal)
Definition for calorie = amount of heat needed to raise 1 gram of water 1 degree C
A food Calorie is actually a kilocalorie or 1000 “little c” calories
Conversion: 1 cal = 4.184 J
3.2 Section Assessment
1. Which five SI base units are commonly used in chemistry?
2. Which metric units are commonly used to measure
length?
volume?
mass?
temperature?
energy?
3. What is the symbol and meaning of each prefix?
kilocentimilli-
4. What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick?
5. State the difference between mass and weight.
6. Surgical instruments may be sterilized by heating at 1700C for 1.5 hours. Convert 1700C to kelvins.