If we round 20.8cm to the nearest centimetre, it becomes 21cm.

If we are given the number 21cm and told it has been previously rounded to the nearest centimetre, we do not know what number it was originally.  For example it could have been 21.2cm, or 20.9cm, or 20.756cm.  What we do know, is the biggest (maximum) or smallest (minimum) number it could possibly have been.

The minimum value it could have been, is 20.5cm.  Any smaller, even a tiny bit, and it would have rounded down to 20cm, not up to 21cm.

The maximum value it could have been, is 21.499999999…cm.  Because this looks messy, we tend to just say the maximum value it could have been before rounding is 21.5cm.  Yes, this would have been rounded up to 22cm, but since the difference between 21.5cm and 21.499…cm is infinitely small anyway, and it looks so much neater, we say the maximum is 21.5cm.

If all the numbers in a calculation have been rounded, then there is a maximum and minimum value for the answer to the calculation.

e.g. 5m x 10m, where both measurements have been rounded to the nearest metre.

Maximum:  5.5m x 10.5m = 57.75m

Minimum: 4.5m x 9.5m = 42.75m

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