This document provides conversions between various units including miles to cm, pm to feet, gallons to cm3, Angstroms to miles, mg to μg, m2 to cm2, μm2 to cm2, mL to pages printed, minutes to sort sheets of paper, g⋅cm3/s2 to kg⋅m3/hour2, g/L to lb/ft3, and m/s to miles/day. It also provides examples of dimensional analysis problems involving multiple conversion steps and significant figures that students will need to solve for a chemistry class.

1. CHM 111 Dimensional Analysis Unit 1 Math Skills Toolbox
Useful Conversions: 4 qts = 1 gal; 0.946 L = 1 qt; 1 mile = 5280 ft; 1 ft = 30.5 cm
39.4 in = 1 m; 1 lb = 0.454 kg 1 in = 2.54 cm, 1 m = 102 cm
1 m = 1012 pm; 1 m = 106 µm; 1 m = 109 nm; 1 km = 103 m
1 mL = 1 cm3; (1 “angstrom”) = 1 Å = 10−10 m 1010 Å = 1 m
Please note that METRIC conversions will NOT be given on exams or quizzes, including
temperature conversions between C and K.
1. a) Convert 150 miles to cm. Remember to express your answer with the correct number of
significant figures. Note that there are multiple ways (routes) to solve this problem.
b) Briefly justify whether or not your answer seems reasonable.
2. a) Convert 341.0 pm to feet. Remember to express your answer with the correct number of
significant figures. Note that there are multiple ways (routes) to solve this problem.
b) Briefly justify whether or not your answer seems reasonable.
3. a) Convert 12.1 gallons to cm3. Remember to express your answer with the correct number of
significant figures. Note that there are multiple ways (routes) to solve this problem.
b) Briefly justify whether or not your answer seems reasonable.
4. Many chemists at a recent conference in Atlanta, Georgia, participated in the 50. trillion Angstrom
Run. How long is this run in miles?

2. CHM 111 Dimensional Analysis Unit 1 Math Skills Toolbox
5. The acidic part of vinegar is acetic acid. If a 10.0 ml vinegar sample contains 483 mg acetic acid,
what is this mass in micrograms (g)?
6. Convert 3.45 m2 to cm2. Remember to express your answer with the correct number of significant
figures. Note that there are multiple ways (routes) to solve this problem.
7. Convert 3.45 µm2 to cm2. Remember to express your answer with the correct number of significant
figures. Note that there are multiple ways (routes) to solve this problem.
8. For a given printer, 1.0 mL of ink is used in printing 50 pages of text. How many pages could be
printed using 100 gallons of ink?
9. A clerk sorts 375 sheets of paper in one hour. How many minutes would it take for the clerk to sort
125 inches of sheets? (There are 225 sheets of paper in each 1 inch stack of sheets.)
10. Convert 10.3 g  cm3/ s2 to kg  m3/ hour2.
11. An air sample taken from a local city contains 3.5  106 g/L of carbon monoxide. What is the
concentration of carbon monoxide in units of lb/ft3?
12. Convert 2.998  108 m/s to miles/day.