Unit Conversions with Significant Digits
SPH3U
Ms. Kueh
Unit Conversions is a very important science concept. These are used heavily in Physics and
Chemistry.
For example, since atoms and molecules are so small, a common unit is moles:
1 𝑚𝑜𝑙 = 6.02 × 1023 entities of a substance
1 𝑚𝑜𝑙 of water = 6.02 × 1023 H2O molecules
We often have to convert from grams or kilograms of a substance to the number of atoms or
molecules.
How many molecules of water are in 5 kg of water?
5 𝑘𝑔 ×
1000𝑔 1 𝑚𝑜𝑙 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 6.02 × 1023 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
×
×
1 𝑘𝑔
18.0153 𝑔
1 𝑚𝑜𝑙 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
= 1.67080204 × 1026 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
Some Standard Conversions
1 hour = 60 minutes
60 seconds
1 meter = 3.28 feet
1 kg = 2.2 lbs
1 m3 = 1 000 000 L
1 mile = 5280 feet
1 foot = 12 inches
1 km = 0.62 miles
1 lb = 0.45 kg
1 year = 365.25 days
1 yard = 3 feet
1 inch = 2.54 cm = 25.4 mm
100 cm = 1 meter
1 quart = 0.946 liters
Note* Sometimes to keep the numbers simple, 365 days is used for 1 year.
You will also need to know the prefixes from the note (Mega, tera, giga, etc.)
1.
Convert 70 𝑘𝑚/ℎ to 𝑚/𝑠.
2. Which is faster, going 80 miles an hour or going 40 meters per second?
3. Do the following metric conversions.
a) 6580000 𝑐𝑚 to 𝑘𝑚
b) 0.065 𝑠 to 𝑚𝑠
c) 5.24 × 108 𝑛𝑚 to 𝐺𝑚
d) 2.43 × 10−6 𝑀𝑚2 to 𝑚2
e) 0.0000076 𝑀𝑔 to 𝑘𝑔
f) 12500 𝜇𝑚 to 𝑐𝑚
g) 7460 𝑚2to 𝑘𝑚2
h) 8560000 𝑐𝑚2 to 𝜇𝑚2
More basic conversion practice.
Convert the following quantities. Round to two decimals where appropriate.
1.
565,900 seconds into days
2.
17 years into minutes
3.
43 miles into feet
4.
165 pounds into kilograms
5.
100 yards into meters
6.
22,647 inches into miles
7.
2678 cm into feet
8.
70 km2 into m2
9.
40 cm3 to m3
10.
4 km2 to mm2
11.
60 miles per hour into meters per second
12.
1100 feet per second into miles per hour
13.
721 lbs per week into kg per second. Round to 6 decimal places.
14.
88 inches per second into miles per day
15.
186,282 miles per second into meters per second
Answers:
1. 19.44 𝑚/𝑠
2. 40 𝑚/𝑠 is faster
3. a) 65.8 𝑘𝑚
d) 2.43 × 106 𝑚2
g) 0.00746 𝑘𝑚2
b) 65 𝑚𝑠
e) 7.6 × 10−3 𝑘𝑔
h) 8.56 × 1014 𝜇𝑚2
c) 5.24 × 10−10 𝐺𝑚
f) 1.25 𝑐𝑚
Basic Conversion Practice
1) 6.55 days
4) 74.25 kg
7) 87.86 ft.
10) 4 × 1012 mm2
13) 0.000536 kg/s
2) 8 935 200 min.
5) 91.46 m
8) 70 000 000 m2
11) 26.88 m/s
14) 120 miles/day
3) 227 040 ft.
6) 0.36 miles
9) 0.00004 m3
12) 750 mph
15) 300 454 838.7 m/s