1. Ch. 3 Notes---Scientific Measurement
Qualitative vs. Quantitative
Qualitative measurements give results in a descriptive nonnumeric form. (The result of a measurement is an _____________ describing the object.)
*Examples: ___________, ___________, long, __________...
Quantitative measurements give results in numeric form. (The results of a measurement contain a _____________.)
*Examples: 4’6”, __________, 22 meters, __________...
Accuracy vs. Precision
Accuracy is how close a ___________ measurement is to the ________ __________ of whatever is being measured.
Precision is how close ___________ measurements are to _________ ___________.
adjective
short
heavy
cold
number
600 lbs.
5 ºC
single
true
value
several
each
other

2. Practice Problem: Describe the shots for the targets.
Bad Accuracy & Bad Precision
Good Accuracy & Bad Precision
Bad Accuracy & Good Precision
Good Accuracy & Good Precision

3. Significant Figures
Significant figures are used to determine the ______________ of a measurement. (It is a way of indicating how __________ a measurement is.)
*Example: A scale may read a person’s weight as 135 lbs. Another scale may read the person’s weight as lbs. The ___________ scale is more precise. It also has ______ significant figures in the measurement.
Whenever you are measuring a value, (such as the length of an object with a ruler), it must be recorded with the correct number of sig. figs.
Record ______ the numbers of the measurement known for sure.
Record one last digit for the measurement that is estimated. (This means that you will be ________________________________ __________ of the device and _____________ what the next number is.)
precision
precise
second
more
ALL
reading in between the
marks
estimating

4. Significant Figures
Practice Problems: What is the length recorded to the correct number of significant figures?
length = ________cm
11.65
(cm)
length = ________cm 58

5. Rules for Counting Significant Figures in a Measurement
When you are given a measurement, you will need to be aware of how many sig. figs. the value contains. (You’ll see why later on in this chapter.)
Here is how you count the number of sig. figs. in a given measurement:
#1 (Non-Zero Rule): All digits 1-9 are significant.
*Examples: g =_____S.F g = _____ S.F.
#2 (Straddle Rule): Zeros between two sig. figs. are significant.
*Examples: 205 m =_____S.F m =_____S.F.
cm =_____S.F.
#3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to the right of a sig. fig. are significant.
*Examples: sec. =_____S.F sec. =_____S.F.
km =_____S.F. 3 2 3 4 5 3 3 4

6. Rules for Counting Significant Figures in a Measurement
#4 (Bar Rule): Any zeros that have a bar placed over them are sig. (This will only be used for zeros that are not already significant because of Rules 2 & 3.)
*Examples: 3,000,000 m/s =_____S.F lbs =____S.F.
#5 (Counting Rule): Any time the measurement is determined by simply counting the number of objects, the value has an infinite number of sig. figs. (This also includes any conversion factor involving counting.)
*Examples: 15 students =_____S.F pencils = ____S.F.
7 days/week =____S.F sec/min =____S.F. 4 2 ∞ ∞ ∞ ∞

7. Steps for Writing Numbers in Scientific Notation
Scientific notation is a way of representing really large or small numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = x 1012 miles
mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
(1) Write down all the sig. figs.
(2) Put the decimal point between the first and second digit.
(3) Write “x 10”
(4) Count how many places the decimal point has moved from its original location. This will be the exponent...either + or −.
(5) If the original # was greater than 1, the exponent is (__), and if the original # was less than 1, the exponent is (__)....(In other words, large numbers have (__) exponents, and small numbers have (_) exponents. + − + −

8. Scientific Notation
Practice Problems: Write the following measurements in scientific notation or back to their expanded form.
477,000,000 miles = _______________miles
m = _________________ m
6.30 x 109 = ___________________ miles
3.88miles x 10−6 kg = __________________ kg
4.77 x 108
9.10 x 10−4 −
6,300,000,000

9. Calculations Using Sig. Figs.
When adding or subtracting measurements, all answers are to be rounded off to the least # of ___________ __________ found in the original measurements.
When multiplying or dividing measurements, all answers are to be rounded off to the least # of _________ _________ found in the original measurements.
Practice Problems:
2.83 cm cm − 2.1 cm = cm ≈_____ cm
36.4 m x 2.7 m = m2 ≈ _____ m2
0.52 g ÷ mL = g/mL ≈ ____ g/mL
decimal places
Example: +
≈ (only keep 2 decimal places)
significant figures
4.7
(only keep 1 decimal place) 98
(only keep 2 sig. figs)
5.9
(only keep 2 sig. figs)

10. The SI System (The Metric System)
Here is a list of common units of measure used in science:
Standard Metric Unit Quantity Measured
kilogram, (gram) ______________
meter ______________
cubic meter, (liter) ______________
seconds ______________
Kelvin, (˚Celsius) ______________
The following are common approximations used to convert from our English system of units to the metric system:
1 m ≈ _________ kg ≈ _______ L ≈ 1.06 quarts
1.609 km ≈ 1 mile gram ≈ _______________________
1mL ≈ _____________ volume 1mm ≈ thickness of a ________
mass
length
volume
time
temperature
1 yard
2.2 lbs.
mass of a small paper clip
sugar cube’s
dime

11. The SI System (The Metric System)

12. kilo- hecto- deka- deci- centi- milli-
Metric Conversions
The metric system prefixes are based on factors of _______. Here is a list of the common prefixes used in chemistry:
kilo- hecto- deka deci- centi- milli-
The box in the middle represents the standard unit of measure such as grams, liters, or meters.
Moving from one prefix to another involves a factor of 10.
*Example: 1000 millimeters = 100 ______= 10 ______ = 1 ______
The prefixes are abbreviated as follows:
k h da g, L, m d c m
*Examples of measurements: 5 km 2 dL 27 dag 3 m mm 10 cm dm m
grams Liters meters

14. 380 km = ______________m 1.45 mm = _________m
Metric Conversions
To convert from one prefix to another, simply count how many places you move on the scale above, and that is the same # of places the decimal point will move in the same direction.
Practice Problems:
380 km = ______________m mm = _________m
461 mL = ____________dL cg = ____________ dag
0.26 g =_____________ mg ,000 m = _______km
Other Metric Equivalents
1 mL = 1 cm L = 1 dm3
For water only:
1 L = 1 dm3 = 1 kg of water or mL = 1 cm3 = 1 g of water
(1) How many liters of water are there in 300 cm3 ? ___________
(2) How many kg of water are there in 500 dL? _____________
kilo- hecto- deka deci- centi- milli-
380,000
4.61
0.0004
260
230
0.3 L
50 kg

15. Metric Volume: Cubic Meter (m3)
10 cm x 10 cm x 10 cm = Liter

16. Area and Volume Conversions
If you see an exponent in the unit, that means when converting you will move the decimal point that many times more on the metric conversion scale.
*Examples: cm2 to m move ___________ as many places
m3 to km move _____ times as many places
Practice Problems: km2 = _________________m2
4.61 mm3 = _______________cm3
k h da g, L, m d c m
twice 3
380,000,000
grams Liters meters

17. Mass vs. Weight
Mass depends on the amount of ___________ in the object.
Weight depends on the force of ____________ acting on the object.
______________ may change as you move from one location to another; ____________ will not.
You have the same ____________ on the moon as on the earth, but you ___________ less since there is less _________ on the moon.
matter
gravity
Weight
mass
Mass = 80 kg
Weight = 176 lbs.
mass
weigh
gravity
Mass = 80 kg
Weight = 29 lbs.

18. Density
Density is a ___________ of an object’s mass and its volume.
Density does not depend on the _________ of the sample you have.
The density of an object will determine if it will float or sink in another phase. If an object floats, it is _______ dense than the other substance. If it sinks, it is ________ dense.
The density of water is 1.0 g/mL, and air has a density of g/mL (or 1.29 g/L).
Density = Mass/Volume
ratio
size
less
more
Mass = D x V m
Density = m/V
Volume = m/D D X V

19. Density Practice Problems:
The density of gold is 19.3 g/cm3. How much would the mass of a bar of gold be? Assume a bar of gold has the following dimensions: L= 27 cm W= 9.0 cm H= 5.5 cm
(2) Which picture shows the block’s position when placed in salt water?
mass = D x V
Volume = L x W x H
mass = 19.3 g/cm3 x cm3 = 25, g
Volume = 27 x 9.0 x 5.5 = cm3
mass ≈ 26,000 g = 26 kg ≈ 57 lbs.
(3) Will the following object float in water? _______
Object’s mass = 27 g
Object’s volume= 25 mL
No! It will sink. (D > 1)

20. Measuring Temperature
Temperature is the ____________ or ____________ of an object.
The Celsius temperature scale is based on the freezing point and boiling point of __________.
F.P.= 0˚C B.P.= 100˚C
The Kelvin temperature scale, sometimes called the “absolute temp. scale”, is based on the ____________ temperature possible, absolute zero. (All molecular motion would __________.)
Absolute Zero = 0˚ Kelvin = −273˚ C
To convert from one temp. scale to another:
˚C = Kelvin − 273
K= Celsius + 273
Practice Problems: Convert the following
25˚C = _______ K
473 K = _______˚C
hotness
coldness
water
lowest
stop
298
( )
(473 – 273)
200

21. Temperature Scales
Liquid Nitrogen

22. Evaluating the Accuracy of a Measurement
The “Percent Error ” of a measurement is a way of representing the accuracy of the value. (Remember what accuracy tells us?)
% Error = (Experimentally Measured Value) − (Accepted Value) x (Accepted Value)
Practice Problem:
A student measures the density of a block of aluminum to be approximately 2.96 g/mL. The value found in our textbook tells us that the density was supposed to be 2.70 g/mL. What is the accuracy of the student’s measurement?
(Absolute Value)
% Error = | | ÷ 2.70 =
…x 100 =
9.63% error