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Is the answer reasonable?
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You know that Shanghai Tower is 632 meters high and that Burj Khalifa is 196 meters higher. You calculate Burj Khalifa's height to be 436 meters. Is that reasonable?
Sometimes if you make a mistake in your calculations. In 1999 NASA's space capsule, Mars Climate Orbiter crashed into the planet Mars. The reason for the crash was that some of the engineers used newton seconds in their calculations, while others used pound seconds. This is like mixing up centimetres and inches. It was an expensive mistake.
It cost over $500 million to build and launch that space capsule. A good way to reduce the risk of mistakes is to test if the answer is reasonable. Leon is filling up the car. Gas costs 15 kronor a litre, the tank holds 55 litres, and it is 20% full. How much will it cost to fill up the car? Leon takes a moment to calculate it, multiplying 55 by 20% by 15 kroner, and concludes that it will cost 165 kronor. Is this reasonable?
No, not really. If gas was 10 kroner per litre, it would have cost 550 kronor to fill up the entire tank. Now he is going to purchase an almost full tank of gas, and the gas is way more than 10 kronor per litre. The answer should be well over 500. You might realize his mistake.
If the tank is 20% full before he fills it up, he needs to fill up 80%. Not 20, 80% of 55 litres times 15 kronor is 660 kronor. This sounds more reasonable. Here we used an estimation in order to test the answer. You can also use your experience to judge a value.
If it usually costs between 500 and 800 kronor to fill up a car then there is a reason to be suspicious if someone says, "It is only going to cost 165 kronor this time." Lena is changing water in a salt water aquarium, and needs to calculate the volume. The aquarium is 47 metres deep, 50 centimetres wide, and one meter long. How many litres of salt water does she need to mix? Lena converts metres to centimetres to get the same units. She multiplies 40 times 50 times 100 and gets a large number starting with two.
The answer is in cubic centimetres, but how many litres is that? If a regular milk carton is one litre, how many cartons of milk would it take to fill the aquarium? Is it 20, 200, or 2000? 20 would barely cover the bottom and 2000 is way too much. 200 seems the most reasonable, and 200 times 1000, since there are 2000 cubic centimetres in one litre, is precisely 200,000 which is what Lena got when she calculated the volume.
Large numbers with a lot of zeroes are easy to miscount. Before you answer think about what is reasonable, and you'll reduce your risk of mixing up kilometres and metres, or kilos and grams. Leon lives five kilometres away from school, and Lena lives a little further away on the same street, six kilometres away from school. When Leon has to calculate how far he has to bike from his house to Lena's house, he takes one distance minus the other, five minus six. He ends up with minus one. Is that reasonable?
No, a distance can never be negative. Six minus five, on the other hand, gives the right answer, one kilometre. Not all numbers can be tested by experience or observation, but you can always do an estimation in order to check if you're close. Make a habit to always test if your answer is reasonable, either by an estimation or any other way that suits the problem.