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You may have heard a climate scientist talking about ‘parts per million’ or ppm. If you want to get a handle on what that means, and how much CO₂ is in our atmosphere, you’ve come to the right place!

Safety: Donate this rice to maths. Don’t eat the black grains.

You will need

• 1 kg rice
• Large jar, big enough to hold all the rice
• Electronic scales
• Plastic container
• Marker
• Calculator

Calculate the mass of a grain of rice

1. Weigh out exactly 10 g of rice.
2. Count the number of grains of rice you weighed out. Count again to make sure.
3. Divide 10 g by the number of rice grains. This gives an estimate of the mass of one grain of rice in g.

   

4. Take this number and multiply it by 1000. Round to the nearest integer (‘whole number’). This is the mass of one grain of rice in mg.

Visualising parts per million

1. Pour all the rice (including the 10 g you weighed) into the jar.
2. Divide 400 by the mass of one grain of rice in mg. This will tell you how many grains of rice make 400 mg.
3. Count out 400 mg of rice and use a marker to colour the grains. Put them back in the jar.
4. Put the lid on the jar, seal tightly, and shake vigorously.
5. Try to spot the coloured rice. If you can’t see them, turn the jar until you can. Is it easy to see all the coloured rice grains?

   

What’s happening?

We can express the concentration of coloured rice in the jar of white rice in terms of mg/kg. There are 400 mg of coloured rice in 1 kg of white rice, so the concentration of coloured rice is 400 mg/kg.

But 1 is the same as one millionth of a kg. So instead of using the unit ‘mg/kg’, we can use parts per million. So 400 mg of coloured rice per kg is 400 ‘ppm by mass’.

When we calculated the mass of one grain of rice we made what’s called an ‘assumption’. That is, we assumed that all the grains of rice have the same mass. If we measured individual grains of rice precisely we would find that not all rice grains have the same mass. In this activity, our assumption is fine, as even though the mass of the rice grains varies, they are quite similar.

Assumptions are used all the time in mathematics and science. They are useful for simplifying problems and making calculations. Care must be taken though – poor or incorrect assumptions can often lead to false or misleading conclusions.

Applications

The unit ppm is used in a variety of scientific fields, especially chemistry and environmental science, for expressing low concentrations. They are particularly useful for monitoring hazardous and risky situations, such as pollutants in water and air. Instead of having to use lots of decimal places, ppm allows concentrations to be expressed in terms of small, familiar numbers, such as units, tens and hundreds.

The concentration of coloured rice in this activity is similar to the current concentration of carbon dioxide in the Earth’s atmosphere. Carbon dioxide levels have risen over the last two hundred years. If this current trend continues it may have serious consequences for climate systems around the Earth.

More information

Want to understand the catastrophic effects of a runaway greenhouse effect? Check out Venus’ cool past!

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