An estimate gives the size of an answer from rough values of the quantities involved. Small errors in each value change the result only a little, so an estimate is good for checking calculations.
How many litres of air do you breathe in one day? Nobody measures every breath. Still, the question has an answer you can work out.
The answer will not be exact. It will be close enough to tell you whether the true value is near a hundred litres, a thousand, or ten thousand. That level of accuracy is called getting the order of magnitude right. Each order of magnitude is a factor of 10.
First, write the answer as a product of quantities you can judge. Air breathed per day = breaths per minute × minutes per day × litres per breath. Then give each quantity a rough value, and multiply.
Three rough values, one useful answer. 14 × 1440 × 0.5 = 10,080 L. Each input can be checked with a simple observation at home.
Before using the sliders below: if your count of breaths per minute was 12 instead of 15, would the final answer change completely?
No. 12 is 20% less than 15, so the answer is 20% smaller. 15 × 1440 × 0.5 = 10,800 L. 12 × 1440 × 0.5 = 8,640 L.
Both are close to ten thousand litres. A 20% error in one input gives a 20% error in the result. It does not change the order of magnitude. This is why an estimate can be trusted for size even when no input is exact.
An estimate should be checked against something independent. Here, that is a published measurement. Physiologists measure the air a resting adult breathes using a sealed mask connected to a gas meter. The result is typically 5 to 8 litres per minute.
Over 1440 minutes, that is 7,200 to 11,500 litres per day. The estimate of 10,080 litres falls inside this range. Two independent sources agree on the size, which is good evidence that the reasoning is sound.
A cross-check. On a scale where each step is a factor of 10, the estimate sits inside the measured band. If the estimate had come out at 300 L or 90,000 L, one of the inputs would be wrong.
How much uncooked rice would feed a family of four for a month, if rice were their only food?
Use these values. An adult needs about 2,000 kilocalories a day; take a child as about 1,500. 100 g of uncooked rice provides about 350 kilocalories.
For two adults and two children, the daily need is about 7,000 kcal. That is 7,000 ÷ 350 = 20 lots of 100 g, or about 2 kg a day. Over 30 days, about 60 kg. The answer is tens of kilograms, not hundreds of grams and not tonnes.
1What is the main purpose of an estimate?
2Roughly how many litres of air does a resting person breathe in a day?
3Why was the estimate compared with the measured value of 5 to 8 litres per minute?
4For each situation, decide whether a rough estimate is enough or an exact value is needed.
5A student calculates that a school bus travels at 4,000 km/h. What should she do?
6In the breathing estimate, changing 15 breaths a minute to 12 does what to the answer?
7Getting an answer right to the nearest factor of 10 is called getting its order of ____ right.
8What is estimation useful for?
More than one answer is correct.
That completes the unit How Science Works.
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