It is important to remember that most measurement is approximate.
If you say your garden is 8 metres long you are rounding to the nearest metre and it could be anything from 7.5 to 8.5 metres long.
Upper and Lower Bounds
The real value can be as much as half the rounded unit above or below the value given.
So, if you are given 5.4cm the upper bound is 5.45cm and the lower bound is 5.35cm.
For 6.0kg you need to go 0.05kg either way so the upper bound is 6.05kg and the lower bound is 5.95kg.
Maximum and Minimum Values
For calculations you must use the upper or lower bounds of each measurement depending on what calculation you are doing.
Addition - For the maximum use the upper bound of each measurement, for the minimum use the lower bound of each measurement.
If a piece of wood measuring 15cm is joined to another piece measuring 12cm you can see the maximum and minimum values of the addition by clicking below.
Subtraction - For the maximum you need the biggest difference between the two measurements i.e. the upper bound of the first number and the lower bound of the second and for the minimum it's the other way round.
David and Steven were given seeds to plant in Biology and decided to see whose would grow the highest. After two weeks they measured them to the nearest centimetre and David's had grown to 11cm whereas Steven's had grown to 15cm. What are the maximum and minimum values of Steven's victory?
Multiplication - Same as for Addition
Division - Same as for Subtraction
If it is a complicated calculation e.g. (32.3 x 42.6) - 12.7 then remember the rules for each separate operation. For a maximum this would be (32.35 x 42.65) - 12.65 (Notice the lower bound was used for 12.7 as it was a subtraction).
Graham has a plank of wood of length 610cm, correct to the nearest 10cm. He uses a cutting machine to cut the plank into pieces, without any wastage. Each piece of wood is of length 15 cm, correct to the nearest half centimetre.
Find the maximum number of pieces of wood that Graham can be certain of getting.