jwallach Unit Conversions

1. Unit Conversions – Part 2

2. Purpose
• Up to now all unit conversion have had a single unit in the numerator. We
will now deal with more complex conversion where there are units in both
the numerator and denominator. For example, we may want to convert 10
meters per second(m/s) to miles per hour (mi/hr). To do this, we will still
use dimensional analysis but must be careful to deal with the units in the
denominator properly.

3. With multiple units, deal with each one
separately.
• Convert 10.0 meters per second to miles per hour.
– Given: 10
𝑚
𝑠
– Asked for:
𝑚𝑖
ℎ𝑟
– Relationships: meters to miles: 1609 m = 1 mi
seconds to hours: 3600 s = 1 hr
– Solution – convert each independently
• First, convert the m to mi.
10.0 𝑚
𝑠
𝑥
1 𝑚𝑖
1609 𝑚
=
0.006215 𝑚𝑖
𝑠
• Second, convert the s to hr.
0.006215 𝑚𝑖
𝑠
𝑥
3600 𝑠
1 ℎ𝑟
= 22.4
𝑚𝑖
ℎ𝑟
– Note: notice that since s was in the denominator in our original number,
we had to cancel it out with s in the numerator of our conversion factor.

4. Multiple conversions can be shown in a single
calculation.
• We can put the entire calculation on a single line:
10.0 𝑚
𝑠
𝑥
1 𝑚𝑖
1609 𝑚
𝑥
3600 𝑠
1 ℎ𝑟
= 22.4
𝑚𝑖
ℎ𝑟
• Note: See how a unit in the numerator always cancels out a similar unit in
the denominator.

5. Pause and Practice
• Convert 34.2 liters per minute
𝐿
𝑚𝑖𝑛
to milliliters per second
𝑚𝐿
𝑠
.
– Relationships:
• 1000 mL = 1 L
• 60 s = 1 min.
• Convert 1.01 grams per mole
𝑔
𝑚𝑜𝑙
to zeptograms per atom
𝑧𝑔
𝑎𝑡𝑜𝑚
.
– Relationships:
• 1 x 1021 zg = 1 g
• 6.022 x 1023 atoms = 1 mole

6. Solution 1 - Make sure the conversion factors
are set-up correctly to cancel units
• Convert 34.2 liters per minute
𝐿
𝑚𝑖𝑛
to milliliters per second
𝑚𝐿
𝑠
.
– Relationships:
• 1000 mL = 1 L
• 60 s = 1 min.
34.2 𝐿
𝑚𝑖𝑛
𝑥
1000 𝑚𝐿
1 𝐿
𝑥
1 𝑚𝑖𝑛
60 𝑠
= 570
𝑚𝐿
𝑠

7. Solution 2 - Do not be afraid of unfamiliar units
– you just need to know the relationships.
• Convert 1.01 grams per mole
𝑔
𝑚𝑜𝑙
to zeptograms per atom
𝑧𝑔
𝑎𝑡𝑜𝑚
.
– Relationships:
• 1 x 1021 zg = 1 g
• 6.022 x 1023 atoms = 1 mole
1.01 𝑔
𝑚𝑜𝑙
𝑥
1 𝑥 1021 𝑧𝑔
1 𝑔
𝑥
1 𝑚𝑜𝑙
6.022 𝑥 1023 𝑎𝑡𝑜𝑚𝑠
= 0.00168
𝑧𝑔
𝑎𝑡𝑜𝑚

8. Now try the exercises.
• Take your time to set-up the problem and make sure your units are
correct.