Introduction: If you took 1 million steps, how many miles have you walked? How are you
going to figure this out? Do you want to go outside and carefully count to 1 MILLION as you
take step after step after step? Dimensional analysis to the rescue! In this lab, you will collect
some data and then use this data as a conversion factor to help you make some pretty unusual
calculations.
Problems:
1) Start by putting your heel against a wall or some marking on the ground and then walk heel to
toe exactly 10 steps. Use a meter stick to measure this distance and record it below as a
conversion factor.
Conversion factor:
10 steps = _______________ cm
Needed Conversions: 1 mi = 5280 ft
1 ft = 12 in
1 in = 2.54 cm
How many steps would it take you to go 1 mile? (Use above clues in a 4 step conversion)
1 mile x __________ x ____________ x ____________ x ______10__steps =
cm
If you took 1 million steps, how many miles would that be?
1,000,000 steps x _____________ x ______________ x ______________ x ______________ =
2) Stack up 10 pennies like pancakes. Use a ruler to measure the height of the stack as a
conversion factor.
Conversion factor:
10.0 pennies = ______________ cm
Needed Conversions: 1 mi = 5280 ft
1 ft = 12 in
1 in = 2.54 cm
How many pennies would make a stack 1 mile high?
1.00 mile x ______________ x ________________ x _______________ x ______________ =
3) Use a meter stick to measure off exactly 20 meters. Use a stop watch to time how long it
takes you to walk this distance, at a normal pace. Record this below as a conversion factor.
Conversion factor:
20.0 m = ________________ seconds
Needed Conversions: 1 mile = 1.6093 km
1 km = 1000 m
1 min = 60 sec
How many minutes would it take you to walk 1 mile?
1.00 mile x _____________ x _________________ x _____________sec x ______________ =
20.0
m
Now let’s use proportions to figure out some more large problems.
4) Using your answer in question #3, calculate how long, in minutes, it would take you to walk a
marathon, which is 26.2 miles?
5) Using your answer in question #1, calculate how many steps it would take you to walk the
Great Wall of China, which is 3,948 miles. (You may want to round and use scientific notation.)
6) Using your answer in question #2, calculate how many pennies it would take to reach the high
side of the Leaning Tower of Pisa, which on its high side is 56.7 m or 0.35 miles?