1. Problem Solving in Chemistry
Dimensional Analysis
Used in _______________ problems.
*Example: How many seconds are there in 3 weeks?
A method of keeping track of the_____________.
Conversion Factor
A ________ of units that are _________________ to one another.
*Examples: 1 min/ ___ sec (or ___ sec/ 1 min)
___ days/ 1 week (or 1 week/ ___ days)
1000 m/ ___ km (or ___ km/ 1000 m)
Conversion factors need to be set up so that when multiplied, the unit of the “Given” cancel out and you are left with the “Unknown” unit.
In other words, the “Unknown” unit will go on _____ and the “Given” unit will go on the ___________ of the ratio.
conversion
units
ratio
equivalent 60 60 7 7 1 1
top
bottom

2. If your units did not ________ ______ correctly, you’ve messed up!
How to Use Dimensional Analysis to Solve Conversion Problems
Step 1: Identify the “________”. This is typically the only number given in the problem. This is your starting point. Write it down! Then write “x _________”. This will be the first conversion factor ratio.
Step 2: Identify the “____________”. This is what are you trying to figure out.
Step 3: Identify the ____________ _________. Sometimes you will simply be given them in the problem ahead of time.
Step 4: By using these conversion factors, begin planning a solution to convert from the given to the unknown.
Step 5: When your conversion factors are set up, __________ all the numbers on top of your ratios, and ____________ by all the numbers on bottom.
Given
Unknown
conversion factors
multiply
divide
If your units did not ________ ______ correctly, you’ve messed up!
cancel out

3. How many hours are there in 3.25 days?
Practice Problems:
How many hours are there in 3.25 days?
(2) How many yards are there in 504 inches?
(3) How many days are there in 26,748 seconds?
24 hrs
3.25 days
78 hrs x =
1 day
1 ft
1 yard
504 in.
14 yards x x =
12 in.
3 ft
1 min
1 hr
1 day
26,748 sec
days x x x =
60 sec
60 min
24 hrs

4. 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

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

6. 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 taking a __________ at what the next number is.)‏
precision
precise
second
more
ALL
reading in between the
marks
guess

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

8. 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

9. The SI System (The Metric System)‏

11. 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 45 mm
mass cm dm m
grams Liters meters

12. Other Metric Equivalents
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 dm3 ? ___________
(2) How many kg of water are there in 500 mL? _____________
380,000
4.61
0.0004
260
230
300 L
0.5 kg

13. 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

14. 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. + − + −

15. 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 = ___________________ miles
3.88 x 10−6 kg = __________________ kg
4.77 x 108
9.10 x 10−4 −
6,300,000,000

16. 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 = (Accepted Value) − (Experimentally Measured 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 = |2.70−2.96| ÷ 2.70 =
…x 100 =
9.63% error