## Guesstimating, or Checking Your Answers Make Sense

Calculate 1234 × 1234

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

1,522,756

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:

153,016

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:

1,522,756

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.