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Scientific notation sprinkles

By David Shaw, 7 April 2017

In everyday life, most numbers we use are less than 1000. Sometimes scientists need to use MUCH larger numbers. Here’s an insight into how they do it.

Safety: If you’re planning to use these sprinkles in cooking, use clean hands and equipment.

You will need

• Jar of hundreds and thousands sprinkles
• Measuring spoons and cup
• Pen
• Sticky notes

What to do

1. These steps will create a geometric sequence of sprinkles. Each pile of sprinkles will be 10 times larger than the previous one.
   

   Count out 10 sprinkles

2. For the first pile, put one sprinkle on the table. Then put a sticky note next to it and label it 10⁰.
3. The second pile is 10 times bigger – so count out 10 sprinkles, and then label it 10¹.
4. The third pile is 10 times bigger again, which is 100 sprinkles. It might take a while to count, but when you’ve finished, label it 10².
   

   one teaspoon can hold about 1000 sprinkles

5. The next pile needs 1000 sprinkles, which is too many to count easily. Luckily, we’ve done the counting for you! There are about 1000 sprinkles in a teaspoon, so just measure out one level teaspoon and label it 10³.
6. Ten times bigger than a teaspoon is 10 teaspoons, but there is a better way to measure it. A teaspoon is 5 mL, so 10 teaspoons is 50 mL. To measure this you could use a measuring cup, or you could measure out two and a half tablespoons. That’s 10 000 sprinkles! Label this pile 10⁴.
   

   There are 10 000 sprinkles in the measuring cup!

7. You might have run out of sprinkles, but if you still have lots to spare, here’s one more pile to measure. There’s 100 000 sprinkles in 500 mL, which is two cups. Label this pile 10⁵.
8. Look at the piles you have. Can you imagine how big the 10¹⁰ pile would be?

What’s happening?

What’s the biggest number you know? A billion? A trillion? You probably don’t use huge numbers very often. But some scientists need to use immense numbers regularly.

In just one gram of hydrogen gas, there are about 602 214 085 700 000 000 000 000 atoms. This number is stupendously large, and yet chemists use it all the time. It’s easy to make a mistake with all the zeros at the end. So instead of writing it all out, they split the number of digits from the digits themselves. Scientists would instead write 6.022 x 10²³.

This way of writing numbers, known as scientific notation, makes calculations a lot easier. And once you’ve had some practice with it, it’s not hard to read. For example, 2.998 x 10⁸ is a number with nine digits, and the first four digits are 2998. This number is important to physicists – it’s the speed of light (in metres per second).

In this activity, the label for each pile tells you how many tens you need to multiply together to get your number. So the 100 sprinkle pile is labelled 10², because 100 is 10 times 10. The one sprinkle pile is 10⁰ to match the pattern – if you multiply it by 10, you get 10¹, which is 10.

And if you’re wondering, the 10¹⁰ pile would be about 50 000 litres, or a pile the size of a large tanker truck!

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