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Measuring money

By David Shaw, 8 October 2013

There are some surprising patterns that can be revealed in Australian coins if you take a closer look.

You will need

If you don’t have lots of coins lying around you can get change from your local bank.

• 100 five cent coins
• 50 ten cent coins
• 25 twenty cent coins
• 10 fifty cent coins
• Tall skinny jar (or drinking glass)
• Permanent marker
• Kitchen scales
• Pen and paper

What to do

1. Count out the correct number of each type of coin and put them in separate piles. Calculate how much each pile is worth.
   

   Shake the jar and then mark the height of the coins.

2. Put all the five cent coins into the jar. Shake the jar to settle the coins. Mark the height of the coins on the side of the jar using the marker and label the mark ‘five cents’. Then empty the jar.
3. Repeat step 2 with each of the other types of coins, changing the label to match the coin type. Which type of coin took up the most room in the jar? Which took up the least?
4. Put all the five cent coins on the scales. Record their mass and then take the coins off the scales.
5. Repeat step 4 with each of the other types of coins. Which type of coin weighed the most? Which weighed the least?
6. Compare the value, volume and mass of each type of coin. Do you notice any patterns?

What’s happening?

Weigh each bag and record the results. Do you notice a pattern?

If you look at Australian silver coins, heavier coins weigh more. For five cent, ten cent and twenty cent coins, the weight of the coin is proportional to the value. This means that five dollars weighs the same, whether it’s made up of five cent, ten cent and twenty cent coins, or a mixture of the three. However, fifty cent coins don’t match the pattern – they are only a few grams heavier than twenty cent coins.

When you put different coins into the jar, you might find they come up to different heights. These jumbled piles of coins all have different volumes. However, the coins themselves are all made of the same metal, and they each weigh the same amount. If you melted the coins down, each pile would have the same volume of metal. The difference comes from how the coins are arranged in the jar, and how big the gaps between the coins are.

Applications

Coins have been around for thousands of years. In many cultures, coins have been made of precious metals such as silver or gold. The value of the coin came from the metal in the coin, so a heavier coin would be worth more. These days, most coins are made of relatively cheap metals, and heavier coins are not always more valuable.

When Australia changed to dollars and cents in 1966, fifty cent coins were round and made of a different metal to five, ten and twenty cent coins. It was uneconomical to continue to make these coins – there was a lot of silver in them and the price of silver increased. When the mint reissued 50 cent coins, they chose a different shape – a dodecagon – to help prevent confusion with 20 cent pieces. This might explain why five dollars worth of fifty cent coins is relatively light.

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