Estimating
We can use significant figures to get an approximate answer to a problem.
We can round off all the numbers in a maths problem to \(1\) significant figure to make 'easier' numbers. It is often possible to do this in your head.
Question
Find a rough answer to \(\frac{{19.4}}{{0.0437}}\)
We first round off both numbers to \(1\) significant figure (\(s.f.\)):
\(19.4 = 20 (\,1\,s.f.)\)
\(0.0437 = 0.04 (\,1\,s.f.)\)
So we now need to make the denominator a whole number. We can do this by multiplying both \(20\) and \(0.04\) by \(100\).
\(\frac{{20}}{{0.04}} = \frac{{20 \times 100}}{{0.04 \times 100}} = \frac{{2000}}{4}\)
Divide everything by \(4\).
\(= \frac{{2000}}{4} = 500\)
The real answer to \(19.4 \div 0.0437 = 443.9359\)... So this was a good estimate.
Now try this one. Remember, the working you do is just as important as the answer.
Question
How would you get an approximate answer for \(386062 \times 0.007243\,?\)
Did you get the answer \(400000 \times 0.007 = 2800\,?\) If so, well done!
You rounded off correctly and worked out the approximate answer.
Rounding to \(1\,s.f.\)
\(386062 = 400000\)
\(0.007243 = 0.007\)
So \(400000 \times 0.007 = 2800\)