# Mass Conversions Chemistry Tutorial

## Key Concepts

• Mass is a direct measure of the amount of matter in an object.
• The SI unit(1) of mass is the kilogram which is given the symbol kg
• Chemists in a laboratory usually deal with much smaller masses than kilograms, often grams (g) or milligrams (mg), so we need to be able to convert from one of these metric units of mass to another.
• Metric units of mass:

⚛ kilograms (kg)

1 kg = 103 g = 1000 g

⚛ grams (g)

1 g = 10-3 kg = 0.001 kg

⚛ milligrams (mg)

1 mg = 10-3 g = 0.001 g

• Some countries routinely use non-metric units such as ounces (oz) and pounds (lb) to measure mass. You may need to know how to convert these non-metric units into metric or SI units.
• Non-metric units of mass:

⚛ ounces (oz)

1 oz = 28.35 g

⚛ pounds (lb)

1 lb = 16 oz = 0.4536 kg

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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:

   factors prefix symbol large → → → → → → → → → → → → small 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto 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

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## 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

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## Converting Non-Metric Units of Mass to Metric or SI Units

You will need to know the following conversion factors:

• 1 ounce = 0.0625 pounds = 28.35 grams

1 oz = 0.0625 lb = 28.35 g

• 1 pound = 16 ounces = 0.4536 kilograms

1 lb = 16 oz = 0.4536 kg

### 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

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(1) SI is the abbreviation for Système Internationale d'Unités. It is a unified version of the metric system agreed upon by the General Conference of Weights and Measures in 1960 and is used world-wide.