SME
Grade 9 Math · Algebra 1
Units, accuracy and precision in measurement and modeling
Use this for “A car goes 45 miles per hour. How many feet per second is that?”
Diagram
Struck through: mi, h, each on a top and a bottom, so they cancel.
The unit left is ft/s.
Each factor is 1 (its top and bottom are the same amount), so the amount does not change.
This is an example. Type your own values to start a new problem.
v
mi/h
×
5280
ft
1
mi
×
1
h
3600
s
=
u
ft/s
Formulas
u
=
v
×
5280
3600
66
=
45
×
5280
3600
Assumptions
•
1 mi = 5280 ft and 1 h = 3600 s exactly, so each conversion factor equals 1.
•
Write each factor with the unit to cancel on the other side of the fraction bar.
•
The units left after cancelling are the answer’s unit: a check that the setup is right.
Step-by-step
WE KNOW
v = 45 mph
FIND
speed in feet per second (u)
Step 1 · Find speed in feet per second (u)
Use u = v × 5280/3600
Multiply by 5280 ft per mi and by 1 h per 3600 s: mi and h cancel, leaving ft/s.
u
=
v
mi/h
×
5,280
ft/1
mi
×
1
h/3600
s
u
=
45
mi/h
×
5,280
ft/1
mi
×
1
h/3600
s
u
=
237,600
ft
3,600
s
u
=
66
ft/s
Check
Put the numbers back in. Both sides should match.
66
=
45
×
5280
3600
✓
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