Guesstimating, or Checking Your Answers Make Sense

OK, so you’ve calculated all your answers for an exam, and you look at your watch and realise that you’ve got 5 minutes left.  You can use these 5 minutes to check some of your answers.  But how do you quickly choose which answers to check?  Well this is where guesstimating comes in.  A quick way to check whether your answer ‘makes sense’ is to estimate what the answer should be.  If your estimated answer is very different from your actual answer, then you know that your answer might be wrong, and that it’s worth going through that question again.  Take the following example:

                                                  Calculate 1234 × 1234

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Now, if you type this into your calculator, you should get something like


But say I make a mistake when I’m typing those numbers into my calculator, and I type in:

                                                          1234 × 124

I get an answer of:


This is obviously not the correct answer of 1,522,756 – in fact it’s almost ten times smaller.  So how do I avoid this happening?  Well the answer is in guesstimating.  So let’s pretend I’m in an exam, I’ve calculated 1234 × 1234 and made a mistake typing it into my calculator, and I get the answer 153,016.

A little while later on, I finish the exam, and realise I still have 10 minutes to go.  So I come back to this question, and I guesstimate the answer.  This is how to do it:

Take the two numbers:

                                                         1234 × 1234

Round them to one significant figure:

                                                         1000 × 1000

Multiply the two significant figures together:

                                                            1 × 1 = 1

And then add on the zeroes in each number - there are 3 zeroes in each 1000, making a total of 6 zeroes, which I add to the ‘1’:

                                                       ‘1’ & ‘000000’

                                                          = 1,000,000

So my guesstimated answer is 1,000,000.  Now, I compare this number with the answer I have already calculated – and whoa!  They are very different numbers – 153,016 is a LOT smaller than 1,000,000!  Also, because both numbers were rounded down when I did my guesstimate, I’d expect that the real answer would be larger than my guesstimate, not smaller.

So, worried, I recalculate 1234 × 1234 and this time I’m extra careful typing everything into the calculator, and I get:


This isn’t too much different than my guesstimate – it’s only 1.5 times larger, and also, it’s larger than my guesstimate, which is what we were expecting. I can feel a lot more confident about my answer now.