Name ______________________________
Date _________________
Period _____
Converting Units using Dimensional Analysis
Every conversion factor can be expressed as a ratio relating the two units (an equivalence statement).
For example:
1 mile = 1.6093 kilometers is an equivalence statement. This leads to two ways of expressing the
conversion factor:
1 mile
1.6093 km
or
1.6093 km. These are both conversion factors (ratios).
1 mile
Use the following equivalence statements to write the two corresponding conversion factors.
Equivalence Statement
Conversion Factor (1) Conversion Factor (2)
1 pound = 453.59 grams
1 quart = 0.94635 liters
1 liter = 1000 milliliters
Problems
Use dimensional analysis to make the following conversions using the steps discussed in class:
1. Write the original number and units. Every number must have units!
2. Multiply by the conversion factor that cancels the original units and leaves the desired units on top.
Conversions Practice:
1. Convert 2.4 pounds to kilograms ______________________________________________________
2. Convert 3150 feet to miles ______________________________________________________
3. Convert 22.91 meters to yards ______________________________________________________
4. Convert 46.2 yards to meters ______________________________________________________
5. Convert 881.2 inches to centimeters ___________________________________________________
6. Convert 17.3 liters to milliliters ______________________________________________________
7. Convert 8.75 liters to gallons ______________________________________________________
8. Convert 762 grams to ounces ______________________________________________________
9. Convert 1043 kilometers to miles _____________________________________________________
10. Convert 22.4 grams to kilograms ______________________________________________________
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Name ______________________________
Date _________________
Period _____
Multi-Step Conversions Using Dimensional Analysis
Sometimes you don’t have a direct conversion factor to get from your given units to your desired units.
You can use two or more conversion factors at once to accomplish your task most efficiently.
Example: You must convert 345 ounces to kilograms. But you have no conversion between the two.
1. Find two conversions that together will take you step-wise to your desired units. In this case:
1 pound = 16 ounces and
1 kilogram = 2.2046 pounds
2. Write your starting number with units. In this case 345 oz
3. Arrange and multiply the conversion factors so that the first cancels your original units, and the
second cancels the intermediate units and leaves you with your desired units.
345 oz x 1 lb . x 1 kg
, = 9.78 kg
16 oz 2.2046 lb
Use two or more conversions factors together to make the following conversions
1. Covert 725 milliliters to gallons _____________________________________________________
2. Convert 2.5 miles to meters ____________________________________________________
3. Convert 6,834 centimeters to miles __________________________________________________
4. Convert 825 ounces to liters _____________________________________________________
Challenge Question:
Our track star can leap 96 cm high. How far is this in miles? Show your conversion as one long
chained dimensional analysis problem.
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