1. Do Now: Create a conversion factor for minutes per hour
Create a conversion factor for milligrams per gram
Create a conversion factor for kilograms per gram

2. International System of Units (SI)
Based on the metric system, units are based on multiples of 10.
Once you understand the prefixes for one unit, you understand them for every unit.
Unlike the English system, where it is seemingly random –
teaspoons in a tablespoon, ounces in a pound, inches in a foot and feet in a yard, etc.

3. 5 SI units most commonly used by chemists are:
Quantity
SI Base Unit
Symbol
Length
meter m
Mass
Kilogram (gram)
kg (g)
Time
second s
Amount of substance
mole
mol
Temperature
kelvin K

4. Important Unit prefixes
1 Kilometer (km) = 1000 meters = 1 x 103 m
100 Centimeters (cm) = 1 x 102 cm = 1 meter
1000 Millimeters (mm) = 1 x 103 mm = 1 meter
1,000,000,000 Nanometers (nm) = 1 x 109 nm = 1 meter
Trick – Only Kilo is bigger than the basic unit of measurement. Everything else you need to remember is smaller.

5. Celsius and Kelvin What is the temperature water freezes in Celsius?
What’s the temperature water boils in Celsius?
This scale was setup by defining the freezing and boiling points of water at 0 and 100, and dividing up the distance between into 100 equal parts, degrees.

6. Celsius and Kelvin
Lord Kelvin ran an experiment and calculated the temperature when particles completely stop moving, commonly referred to as absolute zero. The Kelvin temperature scale set absolute zero as 0 K.
The freezing point of water is 273 K and the boiling point of water is 373 K. There are 100 degrees between water boiling and freezing in both scales.
One degree Kelvin is the same amount of change as 1 degree Celsius. You can interconvert Kelvin and Celsius using the following equation:
K = °C + 273

7. Practice Problems 150 °C is what temperature in Kelvin?
67 K is what temperature in Celsius?
250 K is what temperature in Celsius?
423 K
196 K
-206 °C
-23 °C

8. Dimensional Analysis
Using Dimensional Analysis to convert units. There is no one method that’s best for solving every problem. One of the most general ways to solve problems is through Dimensional Analysis
Dimensional analysis is a way to analyze and solve problems using the units (dimensions) of the measurements.
To see how to use dimensional analysis, let’s see it in action, solving a problem.

9. How would you use Dimensional Analysis to figure out how many seconds there are in one day?
Step 1: Start by listing what we know. We know and what we do not know:
Known:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Unknown:
1 day = ?? seconds
Step 2: Setup a dimensional analysis
1 day x 24 hours x 60 minutes x 60 seconds
1 day hour minute

10. Step 3: Cancel out units and do the math operations:
1 day x 24 hours x 60 minutes x 60 seconds =
1 day hour minute
86,400 seconds (8.64 x 104 sec)
Step 4: Evaluate – Does the answer make sense?
The answer is in seconds, and you’d expect a big number of seconds in a day. Double checking the math, all of the correct units were crossed out, and the conversion factors are all equal to each other.

11. Example 2: how many mg are there in 2. 2 kg
Example 2: how many mg are there in 2.2 kg? Give the answer in scientific notation.
Step 1: Listing Known and Unknown
Known:
Quantity present = 2.2 kg
1 kg = 1000 g
1 g = 1000 mg
Unknown:
2.2 kg = ?? mg
Step 2: Setup Dimensional Analysis
2.2 kg x 1000 g x 1000 mg
1 kg g

12. Step 3: Cancel Units and do the math
2.2 kg x 1000 g x 1000 mg = 2,200,000 mg = 2.2 x 106 mg
1 kg g
Step 4: Evaluate – Does the answer make sense?
The answer is in mg and you’d expect a big number of mg in a kg. Double checking the math, all of the correct units were crossed out, and the conversion factors are all equal to each other.

13. “Dimensional Analysis Song” YouTube video:

14. Practice Problems
Express 3.7 mm in km. Give your answer in scientific notation.
Express 77 cm3 in m3. Give your answer in scientific notation.
The mass of Earth is 5.97 x 1024 kg. How many mg is the mass of Earth?
3.7 x 10-6 km
7.7 x 10-5 m3
5.97 x 1030 mg

15. Converting Fractions
Dimensional Analysis can be used to convert fractions, such as density. It just takes more than one conversion factor. Just follow the unit conversions with your conversion factors.
Example - Convert 3.5 g/mL to mg/L
Step 1 – List known and unknown:
Known:
Have 3.5 g/mL
1000 mg = 1 g
1 L =1000 mL
Unknown:
3.5g/mL = ?? kg/L
Step 2 – Setup the Dimensional Analysis
3.5 g x 1000 mg x 1000 mL
mL g L

16. Step 3 – Cancel units and do the math
3.5 g x 1000 mg x 1000 mL = 3.5 x 106 mg/L
mL g L
Step 4 – Evaluate
The units cancel out correctly
The answer has units labeled
The answer makes sense – mg are smaller so g->mg should increase and mL smaller than L so 1/mL -> 1/L should increase.

17. Practice Problem
A student measures that a cube weighs 2.9 kg and has a volume of
1.7 L. Express the density in g/mL using scientific notation and with the correct number of significant figures.
1.7 x 100 g/mL