You might be asked to find an answer where there is no exact answer and asked to give the number to a degree of decimal places or significant figures. Trial and improvement comes in handy here. Basically you plug in numbers until you find the answer with enough accuracy. The best way to learn it is to look at an example…

Example: Solve y2 + 2y = 40, correct to 1 decimal place.

  • So let’s start with y = 6 – this gives us 48 – so we’re looking for something smaller than 6.
  • Let’s try 5 – which gives us 35 – which is too low

 Now we know the number is between 5 and 6.

  • Let’s try 5.5 – which gives us 41.5 – too big
  • 5.4 give us 39.96

So now we know it is between 5.4 and 5.5 – but to get it to one decimal place we need to work it out one place further

  • Let’s try 5.45 which gives us 40.6025 – too big

Therefore we know the solution is between 5.4 and 5.45.

So the answer to 1 d.p. is 5.4