Units of Mass (and conversions)
How heavy?
When we measure how heavy something is, we work out its mass. Depending on what we are weighing, we may choose a different of measurement. You may like to refresh your memory of which unit of measurement we might use for some objects, where you'll see examples of:
- milligrams (mg)
- grams (g)
- kilograms (kg), and
- tonnes (t)
Converting between milligrams and grams
The smallest unit of measurement is the milligram (mg), and there are $1000$1000 of them in a gram (g). To convert between mg and g, we'll need to either multiply or divide by $1000$1000. When we weigh a pinch of salt, it doesn't even weigh 1 gram, so we might want to express that using milligrams.
How do you remember which one though? This video shows you how to convert from mg to kg, or vice-versa, and how to remember whether to multiply or divide by $1000$1000.
Here's a handy visual to remind you whether to multiply or divide by $1000$1000.
Working with grams and kilograms
When we have objects that start to get heavier, we might want to express their mass using grams or kilograms. There are $1000$1000 grams in a kilogram, so we don't have to remember anything new! When we convert to a bigger unit, we divide by $1000$1000, because we'll end up with less units, but they're bigger. Let's see some examples of how to do this in this video.
Here's our visual for converting from grams to kilograms, and vice-versa.
With all of this multiplying and dividing by $1000$1000, which is the same as $10$103, or $10$10×$10$10×$10$10, it is handy to think of how to multiply and divide by 10 and 100 here, and use that to multiply or divide by $1000$1000.
Kilograms and tonnes
Now we're ready for our heaviest objects yet, kilograms and tonnes. We'll be looking at kilograms (kg) and tonnes (t), and converting between the two. Here are some objects that whose mass we might see in kg or t, or both.
| kilograms (kg) | kilograms (kg) or tonnes (t) | tonnes (t) |
|---|---|---|
 |
 |
 |
How many?
$1$1 tonne = $1000$1000 kilograms, so we will be multiplying or dividing by $1000$1000 , as we have with all of our mass conversions. Let's have a look at how we can convert between kilograms and tonnes.
Picturing the conversions
This handy diagram shows how to convert at each step, and the best thing is, the difference is a factor of $1000$1000 at every step.
- When you convert from a larger unit to a smaller unit (e.g. t to kg), you multiply.
- When you convert from a smaller unit to a larger unit (e.g. g to kg), you divide.
Worked Examples
Question 1
Convert $946$946 grams to kilograms.
$946$946 grams = $\editable{}$ kg
Question 2
Convert $11$11 tonnes into kilograms.
$11$11 t = $\editable{}$ kg
Question 3
The cost of mining gold for a mining company is $\$840$$840 per gram. How much will it cost the company to mine $0.2$0.2 kilograms of gold?