Basic science: understanding numbers

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# 3.2 Rounding

So far in this course, we’ve used terms such as ‘almost’, ‘about’ and ’around’ to describe numbers. They’re approximations, or estimates, which have been simplified, or ‘rounded’, sometimes to the nearest whole number, or sometimes to the nearest 10, or 0.1, in order to report the number appropriately. This is one of the main ways scientists communicate the level of confidence in a number’s accuracy.

For example, if you took out a tape measure and measured the size of the room discussed in Week 2 as 3.1 m × 4.1 m × 1.9 m, the volume would be 24.149 m3. But would you really be confident you knew the size of the room to within 0.001 m3? The tape measure may not have been marked off in very small units, so your measurements may have been to the nearest 10 cm instead, but multiplying numbers tends to increase the number of digits. If you wanted to communicate your confidence in the final number, a more appropriate answer would be 24.1 m3 or even 24 m3. Both of these figures are approximations rounded in two different ways, the first was rounded to ‘numbers after the decimal place’, the second was rounded to a number of ‘significant figures’. Both are valid approaches, and they reflect the level of confidence in the final answer. The next section discusses rounding to decimal places.