MATH 072 Unit Analysis Worksheet

Often when working with formulas the most difficult part of the problem comes when the units in the problem are not the same as the units called for in the answer. For example, a problem may give the measurements in miles, but the answer is to be given in feet. Also, a problem may give information in both feet and miles, but to make any calculations the units must be the same.

Steps to follow:

·  Write what you are given in the form of a fraction on the left-hand side of the paper.

·  Write the units that you are trying to get on the right-hand side of the paper after the equal sign.

·  Choose the facts that will allow you to solve the problem.

·  Allowing the given units to “drive” the problem, write the facts in fraction form, with the units in the denominator matching the units in the numerator of the given information.

·  Cancel units that are the same in the numerator and denominator.

Example: How many miles are there in 1,000,000 inches?

Given: 1,000,000 inches

Wanted: miles

1,000,000 inches = miles

1

Facts needed: 1 foot = 12 inches, 1 mile = 5280 feet.

1,000,000 inches x 1 foot x 1 mile = miles

1 12 inches 5280 feet

1,000,000 inches x 1 foot x 1 mile = 1,000,000 x 1 x 1 miles

1 12 inches 5280 feet 1 x 12 x 5280

= 15.78 miles

NOTE: “x” means times.

Practice problems:

1.  How tall in feet was the tallest man on record, Robert Wadlow (1918-1940,) at 272 cm? (There are 2.54 centimeters in an inch.)

2.  How tall in inches was the tallest woman on record, Zeng Jinlian (1964 – 1982), at 248.3 cm?

3.  List the necessary facts and write as a product of fractions to find out how many seconds in a lifetime of 80 years? (Assume 365.25 days per year.)

4.  How many square inches in a square foot? (Remember that when converting area or volume, you must convert all dimensions. This means squaring the conversion for area and cubing the conversion for volume.)

5.  How many cubic inches in a cubic yard?

6.  How many pounds are in 3 tons? (There are 2,000 pounds in 1 ton)

7.  How many cubic centimeters are in 2 cubic meters?