1. Section 1.4—Converting Units

2. Converting Units
Often, a measurement is more convenient in one unit but is needed in another unit for calculations.
Dimensional Analysis is a method for converting units
You may have learned another method of converting units in math or previous science classes…trust me…learn this one now!
It will help you solve many other chemistry problems later in the class!

3. Equivalents Dimensional Analysis uses equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the other?
1 foot
12 inches

4. Equivalents Dimensional Analysis uses equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the other?
When you put two things that are equal on top & on bottom, they cancel out and equal 1
1 foot
12 inches
= 1

5. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
27 inches  1
= 27 inches

6. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
27 inches  1
= 27 inches
1 foot
12 inches
27 inches 
= 2.25 feet

7. Dimensional Analysis
Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement!
Same physical meaning…it’s the same length either way!
27 inches  1
= 27 inches
1 foot
12 inches
27 inches 
= 2.25 feet
Remember…this equals “1”

8. Canceling
Anything that is on the top and the bottom of an expression will cancel
When canceling units…just cancel the units…
1 foot
12 inches
27 inches 
Unless the numbers cancel as well!
1 foot
12 inches 

9. Steps for using Dimensional Analysis1
Write down your given information
Write down an answer blank and the desired unit on the right side of the problem space 2
Use equivalents to cancel unwanted unit and get desired unit. 3
Calculate the answer…multiply across the top & divide across the bottom of the expression 4

10. Common Equivalents = = = = = = = 1 ft 12 in 1 in 2.54 cm 1 min 60 s
1 hr =
3600 s
1 quart (qt) =
0.946 L
4 pints =
1 quart =
1 pound (lb)
454 g

11. How many grams are equal to 1.25 pounds?
Example #1 1
Write down your given information
Example:
How many grams are equal to 1.25 pounds?
1.25 lb

12. How many grams are equal to 1.25 pounds?
Example #1
Write down an answer blank and the desired unit on the right side of the problem space 2
Example:
How many grams are equal to 1.25 pounds?
1.25 lb
= ________ g

13. How many grams are equal to 1.25 pounds?
Example #1
Use equivalents to cancel unwanted unit and get desired unit. 3
Example:
How many grams are equal to 1.25 pounds?
454 g
1.25 lb 
= ________ g 1 lb
Put the unit on bottom that you want to cancel out!
The equivalent with these 2 units is: 1 lb = 454 g
A tip is to arrange the units first and then fill in numbers later!

14. How many grams are equal to 1.25 pounds?
Example #1
Calculate the answer…multiply across the top & divide across the bottom of the expression 4
Example:
How many grams are equal to 1.25 pounds?
454 g 
568
1.25 lb
= ________ g 1 lb
Enter into the calculator: 1.25  454  1

15. Metric Prefixes
Metric prefixes can be used to form equivalents as well
First, you must know the common metric prefixes used in chemistry
kilo- (k) =
1000
These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc.
deci- (d) =
0.1
centi- (c) =
0.01
milli- (m) =
0.001
micro- (μ) = =
nano (n)

16. Write a correct equivalent between “kg” and “g”
Metric Equivalents
Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix)
kilo = 1000
Example:
Write a correct equivalent between “kg” and “g”
There are two options:
1 kg = 1000 g
1000 kg = 1 g
To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

17. Write a correct equivalent between “kg” and “g”
Metric Equivalents
Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix)
kilo = 1000
Example:
Write a correct equivalent between “kg” and “g”
There are two options:
1 kg = 1000 g
1000 kg = 1 g
“1 kg is kilo-gram”…correct
“kilo- kg is 1 gram”…incorrect
To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”

18. Try More Metric Equivalents
Example:
Write a correct equivalent between “mL” and “L”
milli = 0.001
There are two options:
1 L = mL
0.001 L = 1 mL
Example:
Write a correct equivalent between “cm” and “m”
centi = 0.01
There are two options:
1 cm = 0.01 m
0.01 cm = 1 m

19. Try More Metric Equivalents
Example:
Write a correct equivalent between “mL” and “L”
milli = 0.001
There are two options:
1 L = mL
0.001 L = 1 mL
“1 L is milli-mL”…incorrect
“milli-liter is 1 mL”…correct
Example:
Write a correct equivalent between “cm” and “m”
centi = 0.01
There are two options:
1 cm = 0.01 m
0.01 cm = 1 m
“1 cm is centi-meter”…correct
“centi-cm is 1 m”…incorrect

20. Metric Volume Units
To find the volume of a cube, measure each side and calculate: length  width  height
height
width
length
But most chemicals aren’t nice, neat cubes!
Therefore, they defined 1 milliliter as equal to 1 cm3 (the volume of a cube with 1 cm as each side measurement)
1 cm3 =
1 mL

21. How many grams are equal to 127.0 mg?
Example #2
Example:
How many grams are equal to mg?
127.0 mg
= ________ g
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = g

22. How many grams are equal to 127.0 mg?
Example #2
Example:
How many grams are equal to mg?
0.001 g
0.1270
127.0 mg 
= ________ g 1 mg
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = g
Enter into the calculator:   1
You may be able to do this in your head…but practice the technique on the more simple problems so that you’ll be a dimensional analysis pro for the more difficult problems (like stoichiometry)!

23. Multi-step problems
There isn’t always an equivalent that goes directly from where you are to where you want to go!
Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis!
This way you have fewer equivalents to remember and you’ll make mistakes less often
With multi-step problems, it’s often best to plug in units first, then go back and do numbers.

24. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg?
345 cg
= _______ kg
There is no equivalent between cg & kg
With metric units, you can always get to the base unit from any prefix!
And you can always get to any prefix from the base unit!
You can go from “cg” to “g”
Then you can go from “g” to “kg”

25. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg? g kg
345 cg  
= _______ kg cg g
Go to the base unit
Go from the base unit

26. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg?
0.01 g 1 kg
345 cg  
= _______ kg 1 cg
1000 g
1 cg = 0.01 g
1000 g = 1 kg
Remember—the # goes with the base unit & the “1” with the prefix!

27. How many kilograms are equal to 345 cg?
Example #3
Example:
How many kilograms are equal to 345 cg?
0.01 g 1 kg
345 cg  
= _______ kg 1 cg
1000 g
Enter into the calculator: 345  0.01  1  1  1000
Whenever dividing by more than 1 number, hit the divide key before EACH number!
It doesn’t matter what order you type this in…you could multiply, divide, multiply divide if you wanted to!

28. 0.250 kg is equal to how many grams?
Let’s Practice #1
Example:
0.250 kg is equal to how many grams?

29. 0.250 kg is equal to how many grams?
Let’s Practice #1
Example:
0.250 kg is equal to how many grams?
1000 g
0.250 kg 
= ______ g
250. 1 kg
1 kg = 1000 g
Enter into the calculator:  1000  1

30. Let’s Practice #2
Example:
How many mL is equal to 2.78 L?

31. Let’s Practice #2  1 mL 2.78 L = ______ mL .001 L 2780 1 mL = 0.001 L
Example:
How many mL is equal to 2.78 L? 1 mL
2.78 L 
= ______ mL
2780
.001 L
1 mL = L
Enter into the calculator: 2.78  1  0.001

32. 147 cm3 is equal to how many liters?
Let’s Practice #3
Example:
147 cm3 is equal to how many liters?

33. 147 cm3 is equal to how many liters?
Let’s Practice #3
Example:
147 cm3 is equal to how many liters?
Remember—cm3 is a volume unit, not a length like meters! 1 mL
0.001 L
147 cm3  
= _______ L
0.147 1
cm3 1 mL
There isn’t one direct equivalent
1 cm3 = 1 mL
1 mL = L
Enter into the calculator: 147  1   1  1

34. How many milligrams are equal to 0.275 kg?
Let’s Practice #4
Example:
How many milligrams are equal to kg?

35. How many milligrams are equal to 0.275 kg?
Let’s Practice #4
Example:
How many milligrams are equal to kg?
1000 g 1 mg
0.275 kg  
= _______ mg
275,000 1 kg
0.001 g
There isn’t one direct equivalent
1 kg = 1000 g
1 mg = g
Enter into the calculator:  1000  1  1  0.001