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Making Measurements
Day 1- Tuesday
Measurements in Life
What are some examples of situations in your life that require making measurements? Amount of time it takes to do
something Body temperature when you’re sick Speed of a thrown baseball Distance between the line of
scrimmage and the goal
2 Types of Measurements
There are 2 types of measurements that can be made: Qualitative Quantitative
Qualitative: measurements that do NOT involve the use of numbers and are concerned with characteristics of an object.
Quantitative: measurements that involve numbers and must be determined with an apparatus of some sort.
Qualitative or Quantitative?
It is hot outside. Yesterday I ran 3 miles. It was 102° outside this afternoon. The balloon was big and blue. The paper felt soft on my skin. I need 3.25mm of string for my
project. I am 3 foot 4 inches tall. Wow you’re short!!
Qualitative
Quantitative
Quantitative
Quantitative
Quantitative
Qualitative
Qualitative
Qualitative
Don’t Forget…
Why are units just as important in communicating a quantitative measurement as the number is? A number without a unit is meaningless Ex: 35 °F is cold and 35 °C is hot
Accuracy vs Precision
Accuracy: refers to how close a measured value is to an accepted value
Precision: refers to how close a series of measurements are to one another
Accuracy vs Precision
Ken Sue Jon
Trial 1(g/cm3)
1.54 1.40 1.70
Trial 2(g/cm3)
1.60 1.68 1.69
Trial 3(g/cm3)
1.57 1.45 1.71
Average
(g/cm3)
1.57 1.51 1.70
Who collected the most accurate data?
Who collected the most precise data?
Accepted Value = 1.59 g/cm3
Ken, because his average is closest to the accepted value.
Jon, because his values varied by the smallest amount (0.02 g/cm3.
Scientific Notation Rules
1. The first figure is a number from 1-9.
2. The first figure is followed by a decimal point and then the rest of the figures.
3. Then multiply by the appropriate power of 10.
Scientific Notation
Given: 289,800,000Use: 2.898 (moved 8 places)Answer: 2.898 x 108
Given: 0.000567Use: 5.67 (moved 4 places)Answer: 5.67 x 10-4
Learning Check Express these numbers in Scientific
Notation:1) 405789 2) 0.003 872 3) 3,000,000,0004) 0.000 000 02 5) 0.478260
4.05789 x 105
3.872 x 10-3
3 x 109
2 x 10-8
4.7826 x 10-1
Tuesday – Exit Ticket Convert the following number to
scientific notation 1.) 0.000 000 000 276 2.) 150, 000, 000 3.) Determine if the following set of
data is accurate, precise or both.The bug is 2.59 cm long
3.58 cm3.59 cm3.57 cm
Day 2- WednesdaySignificant Figures
What is the difference between
75.00 mL
75.0 mL
75 mL
Are they all the same number or are they different?
Rounding rules Look at the number
behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
5.87192 Round 2 digits Round 3 digits Round 4 digits
7.9237439 Round 1 digits Round 2 digits Round 4 digits Round 5 digits
Rounding
5.9
5.87
5.872
8
7.9
7.924 7.923
7
How many sig figs are in the following measurements?
458 g
4085 g
4850 g
0.0485 g
0.004085 g
40.004085 g
Learning Check
3
4
3
3
4
8
Significant Figures How do we read the ruler? 4.5515 cm? 4.551 cm? 4.55 cm? 4.5 cm? 4 cm? We needed a set of rules to decide
21 3 4 5
Significant Figure Rules
Rule #1: All real numbers (1, 2, 3, 4, etc.) count as significant figures.
Therefore, you only have to be concerned with the 0
Whether a 0 is significant or not depends on the location of that 0 in the number
Which zeros count?
Rule #2: Zeros at the end of a number without a decimal point don’t count
12400 g (3 sig figs)
Rule #3: Zeros after a decimal without a number in front are not significant.
0.045 g (2 sig figs)
Which zeros count?
Rule #4: Zeros between other sig figs do count.
1002 g (4 sig figs)
Rule #5: Zeroes at the end of a number after the decimal point do count
45.8300 g (6 sig figs)
Significant Figures
Pacific Ocean
When the decimal is Present, start counting with the first nonzero number on the left.
Keep counting until you fall off
Atlantic Ocean
When the decimal is Absent, start counting with the first nonzero number on the right.
Keep counting until you fall off.
Other Information about Sig Figs
Only measurements have sig figs.
A piece of paper is measured 11.0 inches tall.
Counted numbers are exact A dozen is exactly 12
Being able to locate, and count significant figures is an important skill.
Learning Check
A. Which answers contain 3 significant figures?
1) 0.4760 cm 2) 0.00476 cm 3) 4760 cm
B. All the zeros are significant in
1) 0.00307 mL 2) 25.300 mL 3) 2.050 x 103 mL
C. 534,675 g rounded to 3 significant figures is
1) 535 g 2) 535,000 g 3) 5.35 x 105 g
Learning Check
In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
4) 63,000 and 2.1
5) 600.0 and 144
6) 0.0002 and 2000
NO
NO
YES- 2
YES- 2
NO
YES-1
Calculations Using Sig Figs
Addition/ Subtraction
The least accurate measurement determines the accuracy of the answer.
Keep only as many decimal places as the least accurate measurement.
Ex: 12.01 + 35.2 + 6 = 53
Multiplication/ Division
The least precise measurement determines the accuracy of the answer.
Round your answer to the least number of significant figures in any of the factors.
Ex: 1.35 x 2.467 = 3.33
Another Example
First line up the decimal places
Then do the adding Find the estimated
numbers in the problem This answer must be
rounded to the tenths place
If 27.93 mL of NaOH is added to 6.6 mLof HCL, what is the total volume of your
solution?
27.96 mL+ 6.6 mL
34.6 mL
34.56 mL
135 cm x 32 cm = 4320 cm2
3 S.F. 2 S.F.Round off the answer to 4300 cm3 which is 2 sig
figs.
Example:
1. 2.19 m X 4.2 m =
A) 9 m2 B) 9.2 m2 C) 9.198 m2
2. 4.311 cm2 ÷ 0.07 cm = A) 61.58 cm B) 62 cm C) 60 cm
3. (2.54 mL X 0.0028 mL) =
0.0105 mL X 0.060 mL
A.) 11.3 mL B)11 mL C) 0.041mL
Learning Check
Percent Error
Percent error is a way for scientists to express how far off a lab value is from the commonly accepted value.
The formula is: % Error = |Accepted value – Experimental Value| x
100 %
Accepted Value
Percent Error
Example 1: Experimental Value = 1.24 g Accepted Value = 1.30 g
% Error = |Accepted value – Experimental Value| x 100 %
Accepted Value
% Error = |1.30 – 1.24| x 100 % 1.30
= 4.62 %
Wednesday- Exit Ticket
How many sig figs are in the following number
1.) 45.00 2.) 4,500 3.) 0.04500 4.) 0.000 00045
Day 3- Thursday
Why do we need common units?
It is important for scientists around the world to be able to communicate with each other!
If we all used a different set of units, communication would be different if not impossible.
Therefore...
International System of Units
The common system of units scientists have devised in order to communicate with each other even when they’re from different places is called the Systemme Internationale (International System in French) or SI.
This system has seven base units that are based on an object or event in the physical world.
SI Base Units
Quantity SI Base Unit Symbol
Time second s
Length meter m
Mass kilogram kg
Temperature Kelvin K
Amount of Substance
moles mol
Electric Current Ampere A
Luminous Intensity candela cd
Time
The SI base unit for time is the second, s.
How is this unit officially defined? The frequency of microwave radiation given off by a
cesium 133 atom is the physical standard used to establish the length of a second.
This is why atomic (cesium) clocks are more accurate than the standard clocks and stopwatches we normally used to measure time.
Length
The SI base unit for length is the meter, m. How is this unit officially defined?
A meter is the distance that light travels through a vacuum in 1/299792458 of a second.
If you need to measure length that is longer than this base unit… you’d measure in kilometers (km).
If you need to measure length that is a shorter distance than the base unit… you’d measure in centimeters (cm) or millimeters (mm).
Mass
Mass is the measure of the amount of matter in a sample.
The SI base unit for mass is the kilogram, kg.
How is this officially defined? The kilogram is defined by a platinum-iridium metal
cylinder stored in Sevres, France. A copy is kept at the National Institute of Standards and Technology in Gaithersburg, Maryland.
Mass
What units are you most likely to use to measure mass in lab? The masses measured
in lab are often much smaller than a kg, for those cases we use grams (g) or milligrams (mg)
Temperature
The SI base unit for temperature is the Kelvin, K.
This scale was calibrated so that changing one unit on the Kelvin scale is the same as changing a temperature by one degree Celsius.
Defining temperature points Celsius: 0° water freezes, 100° water boils Kelvin: 273 water freezes, 0 all motion stops
Temperature
Why was the Kelvin scale invented/ why is it useful? We needed an “absolute zero scale” so that we could do
calculations without negative numbers.
Convert between Kelvin and Celsius K = °C + 273 °C = K – 273
A third temperature scale that we will not use in the lab is Fahrenheit.
How do you convert between Celsius and this scale? °F = (1.8 x °C) + 32 °C = (°F-32) / 1.8
History of Temperature
Lord Kelvin Anders Celsius
Derived Units
Not all quantities can be measured with base units.
Example: the SI unit for speed is meters per second (m/s). Notice that this includes 2 base units- the meter
and the second.
A unit that is defined by a combination of base units is called a derived unit.
Volume
Volume is space occupied by an object.
The derived SI unit for volume is the cubic meter, m3, which is represented by a cube whose sides are all one meter in length.
This unit is much larger than what will commonly be needed in the lab so a more useful derived unit, the cubic centimeter, cm3 is used.
The unit cm3 works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes. The metric unit for volume is the Liter, L.
What are the conversions between volume units? 1000m = 1 L; 1 cm3 = 1 mL; (memorize 1 cm3 1 mL)
Metric Dimensional Analysis
Trick Name/ Symbol Factor
King Kilo (K) 1000 or 103
Henry Hecto (H) 100 or 102
Died Deca (D) 10
By base 1
drinking deci (d) 1/10
chocolate centi (c) 1/100 or 1/102
milk milli (m) 1/1000 or 1/103
Micro (µ) 1/1000000 or 1/106
Nano (n) 1/1000000000 or 1/109
Mass, distance, time, volume, and quantity (amount) are the ones most common to chemistry.
These measurements each have their own base unit.
We want to know/measure
What it’s called
Standard system Metric Base Unit Abbreviation
How much something weighs
Mass Pounds, ounces, tons
Gram g
How long/short something is
Distance Inches, feet, miles Meter m
How much space something takes
up
Volume Pints, gallons, quarts, cups
Liter L
How long something takes
Time Seconds, minutes, hours
Second s
How many of something we
have
Quantity Dozen, gross Mole mol
#2
950 g = ________ kg
Symbol Factor
K 1000
H 100
D 10
b 1
d 1/10
c 1/100
m 1/1000
950 g x
kg
g
=
1
1000
0.95 kg
The greater unit gets the 1
#1
35 mL = _________ cL TWO prefixes = TWO
steps
35 mL x 1 L
1000
mL
x 100cL
1 L
The greater unit gets the 1
= 3.5 cL
Symbol Factor
K 1000 or 103
H 100 or 102
D 10
b 1
d 1/10
c 1/100 or 102
m 1/1000 or 103
μ 1/1000000 or 106
C
C
#8
0.005 kg= _________ dag TWO prefixes = TWO
steps
Symbol Factor
K 1000 or 103
H 100 or 102
D 10
b 1
d 1/10
c 1/100 or 102
m 1/1000 or 103
μ 1/1000000 or 106
0.005 kg
x 103 g
1 kg
C
x 106μg
1 g
The greater unit gets the 1
C
C
= 5x106 μg
Friday- Exit Ticket
Perform the following metric conversion
180 ns to ks 77.2 cm3 to L
Round the following number to 3 sig figs
45674
Extra Dimensional Analysis
Dimensional Analysis
Many problems in chemistry do not have a simple formula that you can plug the data into and get the answer. Instead, solving a chemistry problem requires planning, much like taking a trip. You must determine where you are going (what you are solving for) and how you are going to get there (what do you need to know to solve the problem).
Dimensional Analysis
In chemistry most data is in the form of a measurement. A measure contains two parts - the number and the UNIT!
Many problems involve converting measurements from one unit (or dimension) to another. These units help you to plan the solution to the problem you are trying to solve. The technique of converting between units is called DIMENSIONAL ANALYSIS.
Dimensional Analysis
When you use dimensional analysis to solve chemistry problems you will keep track of the units involved in the calculations you use. When you multiply or divide numbers with units you also multiply or divide the units. You cancel units the same way that you cancel the numerators and denominators of fractions.
A conversion factor is a relationship between different units of measure.
Dimensional Analysis
Give an example of a conversion factor and show 3 ways of writing it.
Inches and feet
Minutes and seconds
Dimensional Analysis
1. Write the given.
2. Set up your conversion factor your units will cancel out.
3. Multiply by factors on the top and divide by factors on the bottom.
Be sure your units are cancelling out and that the unit you’re left with is the desired unit.
Dimensional Analysis
How many inches are equal to 4.5 feet? How many steps? 1 (12 in = 1 ft)
4.50 ft
x 12 in
1 ft
= 54 in
Dimensional Analysis
How many dollars are in 140 dimes? How many steps? 1 (1 dollar = 10 dimes)
140 dimes
x 1 dollar
10 dimes
= 14 dollars
Dimensional Analysis
Pistachio nuts cost $6.00 per pound. How many pounds of nuts can be bought for $20.00? How many steps? 1 (1 pound = $6.00)
20 dollars x 1 pound
6 dollars
= 3.33 pounds
Dimensional Analysis
How much does 4.15 pounds of pistachio nuts cost? How many steps? 1 (1 pound = $6.00)
4.15 pounds
x 6 dollars
= 24.90 dollars
1 pound
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