DIMENSIONAL ANALYSIS, PART 1
Lesson 1: Unit Conversions
The key to making conversions is to use a unit rate, such as 12 inches to 1 foot (example a) or
approximately 1.057 quarts to 1 liter (example d). Notice those unit conversion relationships are equal,
which makes fractions equal to 1 (the numerator and denominator are equal to each other, even though
they look different). Using the number 1 doesn’t change the actual material, length, or time in a
problem—but you get to use the 1 in a form that’s useful to you, that allows you to cancel the units you
don’t want and keep what you do want.
Remember that the order of the numerator and denominator depends on what you want to cancel out.
Notice that in example 1 you have to put feet in the denominator of the second fraction in order to
cancel feet in the first fraction…but then you must put 12 inches in the numerator so that the fraction
equal 1.
After that, it’s a just a matter of multiplying—but don’t lose the correct units; you need them as part of
the answer at the end.
Study the four examples (a to d) and then do the problems at the end.
a. Standard Conversions
Example: How many inches are in 3.5 feet?
3.5 ft. = _____ in.
3.5 ft.
3.5 ft.
1
•
= _____ in.
1 ft.
12 in.
•
1
3.5
12 in.
•
1
= _____ in.
1 ft.
12 in.
Use the conversion rate of 1 foot = 12 inches.
= 3.5 • 12 in. = 42 in.
1
b. Metric Conversions
Example: Convert four and a quarter meters to millimeters.
4.25 m = _____ mm
4.25 m
1
4.25 m
1
4.25
1
•
•
•
1000 mm
1m
1000 mm
1m
1000 mm
1
Use the conversion rate of 1 meter = 1000 millimeters.
= _____ mm.
= _____ mm.
= 4250 mm
c. Standard to Metric Conversions
Example: Convert 25 miles to kilometers.
25 miles = _____ km
25 mi
•
1
25 mi.
•
1
25
1
•
1.6 km
≈ _____ km
1m
1.6 km
≈ _____ in.
1 mi
1.6 km
1
Use the conversion rate of 1 mile = 1.6 km.
≈ 25 • 1.6 km = 40 km
d. Metric to Standard Conversions
Example: How many cups are in 10 liters?
10 liters = _____ cups
Use the conversion rates of 1 liter (L) = 1.057 quarts, and 4 cups = 1
quart. You can choose to use 2 pints = 1 quart and 2 cups = 1 pint, or 1 L = 4.2268 cups, but this
example uses 4 quarts = 1 cup.
10 L
1
10 L
1
10
1
•
•
•
1.057 q
1L
1.057 q
1L
1.057
1
•
•
•
4 cups
1q
4 cups
1q
4 cups
1
≈ _____ cups
≈ _____ cups
≈ 10 • 1.057 • 4 cups = 42.28 cups
Dimensional Analysis Part 1 (Conversions)
Practice Assignment
Directions:




Do these problems on separate paper.
Write the problems on the paper.
You must show your work, by setting up the fractions as in the examples above.
You may use a calculator to do the multiplication/dividing, but do not use online conversion
calculators for this exercise; you must show that you understand how to set up these conversions.
1. How many feet are in 3 miles (statute miles)?
2. How many fluid ounces are in a gallon?
3. Convert 120 ounces to pounds.
4. Convert 7,500 centimeters to meters.
5. How many liters are in 42,780 milliliters?
6. How many grams are in 90 kilograms?
7. Convert 5 cubic yards to cubic meters.
8. Convert 1000 inches to meters.
9. How many ounces are in 100 kilograms?
10. Convert 10 kilometers into feet.
11. Convert 1,000,000 cm into miles.
12. Convert 5,000 milliliters into gallons.