3.1 The importance of estimations

Estimation is an important skill and used quite often in everyday life. In fact, a lot of the time estimation is more important than performing precise calculations. In some situations, you can only make an estimate and often this requires a bit of experience to do well. For example, a paramedic may need to estimate the weight of a patient very quickly by eye (imagine a non-responsive accident victim at a roadside) to determine the dose of drug to administer to them.

However, when calculators or computers are being used, estimation is essential to be able to judge if the output is reasonable. You can estimate by rounding numbers to make them simpler, allowing you to quickly perform the calculation in your head. You can then get a sense of whether your precisely calculated answer is reasonable or not. Get into the habit of doing this – you will find it easier with practice.

Now try an estimation ‘sanity check’ on the next scenario.

You have 2 l of a 2 M stock solution of NaCl but need 500 ml of a 0.2 M solution of NaCl. How much of your stock solution would you need to use to prepare your final solution?

In the above problem, the answer must be less than 500 ml. Since you are making a dilution the volume of stock solution required must be less than the volume of the final solution! It is very easy to invert an operation and divide instead of multiply or vice versa resulting in a nonsensical answer.

Order of magnitude

If one amount is an order of magnitude larger than another, it is approximately 10 times larger. If it is two orders of magnitude larger, it is approximately 100 times larger. For example, an average mouse is around 20 g or 0.02 kg. An average human weighs around 70 kg. You could say that humans are approximately three orders of magnitude larger than mice.

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