Trial & Improvement

 

This is a way of finding the solution to an equation or a puzzle by “educated guesswork”.  Always arrange your work in a table.  Use common sense to make a reasonable first guess

 

eg.1      solve  

            first guess  to 2dp

 

3	27	too big
2	8	too small

 must be between 2 and 3, but closer to 3, so try 2.8

 

 

2.8	21.952	too big  try 2.7
2.7	19.683	too small

 must be between 2.7 and 2.8 so try 2.75

 

2.75	20.796875	too big  try 2.74
2.74	20.570824	too big  try 2.73
2.73	20.346417	too big  try 2.72
2.72	20.123648	too big  try 2.71
2.71	19.902511	too small

 must be between 2.71 and 2.72 etc

 

Look at the question to see how many decimal places are needed for  and keep going until you have an answer that is more accurate and then round off.  For this example, the answer needs to be to 2dp, so we need one more decimal place to know whether to round up or down.

 

So, try  , which is too big.  This means that  must be less than 2.715 ie. 2.714 or lower.  2.714 rounds down to 2.71 so the answer is  (2dp)

 

eg.2 solve  (2dp)

2	6	too small  try 3
3	12	too big  try 2.8
2.8	10.64	too small  try 2.9
2.9	11.31	too big  try 2.85
2.85	10.972	too small  try 2.86
2.86	11.039	too big  try 2.855
2.855	11.006	too big  try 2.854

   or lower

           (2dp)