Chemistry Reference
In-Depth Information
minutes
in the denominator to cancel the
minutes
in the quantity given. It should
also have the unit
hour
in the numerator so that the answer is in hours:
1 hour
60 minutes
Definition
of hour
Minutes
Hours
5445 minutes
a
b
90.75 hours
Any units in the denominator are divided into units in the numerator, just
as any number in the denominator is. Any units and any numbers in the numer-
ator are multiplied. (If a quantity, such as 5445 minutes, is given with no denom-
inator, the quantity is considered to be in a numerator.)
Practice Problem 2.1
Change 5445 minutes to seconds (s).
Aratio or rate may be inverted (turned upside down) if the units that need
to be canceled call for that.
EXAMPLE 2.2
Calculate the time required for a student aide to earn $483 at $11.50 per hour.
Solution
First, put down the quantity given; then multiply it by a factor involving the
rate:
Dollars
Rate
Hours
1 hour
11.50 dollars
483 dollars
a
b
42.0 hours
In this case, the inverse of the rate of pay (the factor used previously to calcu-
late total wages) is employed. Rates or ratios can be used either right side up
or upside down; getting the units to cancel properly will indicate which form
to use. Just be sure that the number in the rate (such as 11.50) stays with the
proper unit (dollars).
Practice Problem 2.2
Calculate the time required to travel 15.0 miles
at 60.0 miles per hour (mph).
EXAMPLE 2.3
Explain why the factor label method works, using the conversion of $2.67 to
cents as an example.
Solution
Consider this equality:
1 dollar
100 cents
Dividing both sides of this equation by $1 yields
100 cents
1 dollar
1
