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Converting Metric and SI Units of Mass
Kilograms (kg), grams (g) and milligrams (mg) are all common units of measuring mass in many countries that have adopted the metric system such as Australia.
For example, if you buy bananas the price is displayed per kilogram, say $3 per kilogram (which in Australia we would say is $3 per kilo of bananas).
If you look on the nutrition panel of a box of sultanas, for example, it will tell you the energy, carbohydrate, protein, and fat content per 100 grams of sultanas.
When you buy medicines, the mass of the active ingredient is usually given in units of milligrams (mg), for example, 200 milligrams (200 mg) of aspirin per tablet.
There are 1,000 grams in 1 kilogram, kilo is a prefix used to indicate 1,000.
We can represent that mathematically as
1,000 grams = 1 kilogram
The unit of mass known as the gram is given the symbol g while the prefix kilo is given the symbol k so a kilogram is represented by the symbol kg.
1,000 g = 1 kg
If you buy ½ kg of bananas, then in grams you would have:
½ × 1,000 g = ½ × 1 kg
500 g = ½ kg
Using scientific notation (exponential notation) we would write:
1 × 103 g = 1 kg
½ × 1 × 103 g = ½ × 1 kg
½ × 103 g = ½ kg
0.5 × 103 g = ½ kg
5 × 102 g = ½ kg
So ½ kg of bananas is the same as 500 g of bananas, or 5 × 102 g of bananas.
We have converted the mass of bananas in kilograms (kg) to a mass of bananas in grams (g).
If 1,000 g = 1 kg then;
1,000 g ÷ 1,000 = 1 kg ÷ 1,000
1 g = 1/1,000 kg
1 g = 1 × 10-3 kg
100 g of sultanas is therefore
100 × 1 g = 100 × 1 × 10-3 kg
100 g = 100 × 10-3 kg
100 g = 1 × 10-1 kg
100 g = 0.1 kg
That is, 100 g of sultanas is the same as 1 × 10-1 kg or 0.1 kg of sultanas.
We have converted the mass of sultanas from units of grams (g) to units of kilograms (kg).
If you look in your medicine cabinet you will probably find tablets containing either aspirin, or paracetamol (acetaminophen), or ibuprofen.
The mass of the active ingredient in each tablet is usually given in units of milligrams (mg), for example 200 mg.
The prefix "milli" is used to represent 1/1000 or 10-3 so 1 milligram is a thousandth of a gram:
1 mg = 1/1000 g = 1 × 10-3 g
200 mg of aspirin is therefore:
200 × 1 mg = 200 × 1 × 10-3 g
200 mg = 200 × 10-3 g
200 mg = 2 × 10-1 g
200 mg = 0.2 g
Since 1 g = 1 × 10-3 kg
200 mg = 0.2 g = 0.2 × 1 × 10-3 kg
200 mg = 0.2 g = 0.2 × 10-3 kg
200 mg = 0.2 g = 2 × 10-4 kg
200 mg = 0.2 g = 0.0002 kg
We have converted the mass of aspirin from units of milligrams (mg) to units of grams (g) and to units of kilograms (kg).
Although kilograms (kg) is the SI unit of mass, chemists routinely use both larger and smaller units for mass.
The factor, prefix, and symbol for each of these is given in the table below:
| |
large |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
→ |
small |
| factors |
1012 |
109 |
106 |
103 |
102 |
101 |
10-1 |
10-2 |
10-3 |
10-6 |
10-9 |
10-12 |
10-15 |
10-18 |
|---|
| prefix |
tera |
giga |
mega |
kilo |
hecto |
deca |
deci |
centi |
milli |
micro |
nano |
pico |
femto |
atto |
|---|
| symbol |
T |
G |
M |
k |
h |
da |
d |
c |
m |
µ |
n |
p |
f |
a |
|---|
This means that:
| 1 kilogram (1 kg) = 103 grams (1000 g) |
1 gram (1 g) = 1 ÷ 103 kilograms = 0.001 kg |
| 1 milligram (1 mg) = 10-3 grams (0.001 g) |
1 gram (1 g) = 1 ÷ 10-3 milligrams = 1,000 mg |
| 1 microgram (1 µg) = 10-6 grams |
1 gram (1 g) = 1 ÷ 10-6 micrograms = 106 µg |
Worked Examples of Mass Conversions Using Metric and SI Units
Question 1:
Convert 1 kilogram to a mass in grams.
Solution:
From the table above we see that kilo = 103 = 1,000
1 kg = 103 g = 1,000 g
Answer 1 kg = 1 000 g
Question 2:
Convert 2.5 kg to a mass in grams
Solution:
From the table: 1 kg = 103 g = 1,000 g
Multiply each term in the equation above by 2.5
2.5 × 1 kg = 2.5 × 103 g = 2.5 × 1,000 g = 2,500 g
Answer 2.5 kg = 2 500 g
Question 3:
Convert 5 milligrams to a mass in grams
Solution:
From the table above we see that milli = 10-3
1 milligram = 1 × 10-3 g = 0.001 g
Multiply each term in the equation by 5
5 mg = 5 × 10-3 g = 0.005 g
Answer 5 mg = 0.005 g
Question 4:
Convert 250 g to a mass in kilograms
Solution:
From the table above we see that kilo = 103
1 kilogram = 1 × 103 g
Divide both terms by 103 to find how many kilograms in 1 g
1 kg ÷ 103 = 103 g ÷ 103
10-3 kg = 1 g
Multiply both sides of the equation by 250
250 × 10-3 kg = 250 g
2.5 × 10-1 kg = 250 g
0.25 kg = 250 g
Answer 250 g = 0.25 kg
Question 5:
Convert 25 µg to a mass in kilograms
Solution:
From the table above we see that micro = 10-6
1 microgram = 1 × 10-6 g
Multiply both sides of the equation by 25
25 µg = 25 × 10-6 g = 2.5 × 10-5 g
Now, kilo = 1000
So, 1 kg = 103 g
And, 1 g = 10-3 kg
Therefore we multiply the mass in g by 10-3 to get the mass in kg:
25 µg = 2.5 × 10-5 g = (2.5 × 10-5) × 10-3 kg
25 µg = 2.5 × 10-5 g = 2.5 × 10-8 kg
Answer 25 μg = 2.5 × 10-8 kg
Converting Non-Metric Units of Mass to Metric or SI Units
You will need to know the following conversion factors:
Worked Examples of Conversion Between Non-Metric Units and Metric or SI Units of Mass
Question 1:
Convert 10 ounces to a mass in grams
Solution:
1 oz = 28.35 g
Multiply both sides of the equation by 10
10 × 1 oz = 10 × 28.35 g = 283.5 g
Answer 10 oz = 283.5 g
Question 2:
Convert 2.5 pounds to a mass in kilograms
Solution:
1 lb = 0.4536 kg
Multiply both sides of the equation by 2.5
2.5 × 1 lb = 2.5 × 0.4536 kg = 1.134 kg
Answer 2.5 lb = 1.134 kg
Question 3:
Convert 900 grams to a mass in pounds
Solution:
1 lb = 0.4536 kg
Divide both sides of the equation by 0.4536 to find how many pounds are in 1 kg
1 lb ÷ 0.4536 = 0.4536 kg ÷ 0.4536
2.2046 lb = 1 kg
Now, 1 kg = 103 g
So, 2.2046 lb = 103 g
Divide both sides of the equation by 103 to find how many pounds are in a gram
2.2046 lb ÷ 103 = 103 g ÷ 103
2.2046 × 10-3 lb = 1 g
Multiply both sides of the equation by 900
900 × 2.2046 × 10-3 = 900 × 1 g
1.984 lb = 900 g
Answer 900 g = 1.984 lb
Question 4:
Convert 0.25 pounds to a mass in milligrams
Solution:
1 lb = 0.4536 kg
Multiply both sides of the equation by 0.25
0.25 × 1 lb = 0.25 × 0.4536 kg
0.25 lb = 0.1134 kg
Now, 1 kg = 103 g
So 0.25 lb = 0.1134 kg = 0.1134 × 103 g
0.25 lb = 113.4 g
Now, 1 g = 103 mg
0.25 lb = 113.4 g = 113.4 × 103 mg = 1.134 × 105 mg = 113 400 mg
Answer 0.25 lb = 113 400 mg
Question 5:
Convert 430 milligrams to a mass in ounces
Solution:
1 oz = 28.35 g
Divide both sides of the equation by 28.35 to find how many ounces are in 1 g
1 oz ÷ 28.35 = 28.35 g ÷ 28.35
0.03527 oz = 1 g
Now, 1 g = 103 mg
So, 0.03527 oz = 103 mg
Divide both sides of the equation by 103
0.03527 oz ÷ 103 = 103 mg ÷ 103
3.527 × 10-5 oz = 1 mg
Multiply both sides of the equation by 430
430 × 3.527 × 10-5 oz = 430 × 1 mg
0.0152 oz = 430 mg
Answer 430 mg = 0.0152 oz
