We round numbers because we’re simple creatures who don’t like working with big, awkward, messy looking numbers. Rounding to a number of decimal places isn’t a very powerful tool, though. What if our number didn’t have any decimal places to begin with?

Instead, there is a more powerful idea, called ‘rounding significant figures’, which sounds complicated, yet you do it all the time in daily life without thinking about it.

The population of the UK is 60 million.

Well, do you really think it’s exactly 60,000,000 people? …of course it isn’t. The real population is 62,218,761.

When cooking, if you’ve measured out 252g of flour, you’d rarely say ‘There’s two hundred and fifty two grams of flour.’ You automatically round it to 2 significant figures without thinking about it, and call it 250g.

We do this because those extra numbers aren’t important. What’s important depends on what you’re doing. If you were the government running a census, then actually knowing there are precisely 62,218,761 people in the country would be very important! But if you’re just comparing rough sizes of countries, knowing the UK has about 60 million people, and the US has 300 million, is enough.

We keep the digits that we think are ‘significant’ (important) and turn all the rest into 0.

Significant Figures (S.F.) Method

Obviously all numbers are significant, but when it comes to rounding, some are more significant than others.

The method for significant figures is identical to that for decimal places (see previous topic) except that finding the position of the LAST DIGIT is more difficult - it wouldn't be so bad, but for the zeros!

  1. The 1st significant figure of any number is simply THE FIRST DIGIT WHICH ISN'T A ZERO.
  2. The 2nd, 3rd, 4th, etc. significant figures follow on immediately after the 1st, REGARDLESS OF BEING ZEROS OR NOT ZEROS.
  3. After rounding off the LAST DIGIT, end ZEROS must be filled in up to, but not beyond, the decimal point.

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