Using a placeholder to enable exchanging
When subtracting a number from one with fewer decimal places, either of the following two errors are likely to occur if a placeholder isn’t used to align the final decimal place and maintain place value .
In example 1, without a place holder above the 3, the pupil has seen a 3 with nothing else and has assumed 3 - 0 = 3, or that there will just be a 3 in the answer.
In example 2, the pupil has realised that subtracting 3 from nothing means needing to exchange, but as there is no placeholder in the column, this results in the exchanged 1 being placed there and the calculation being read as 1 - 3. Exchanging must be repeated a second time and now produces 11 - 3.
Pupils need to understand that the exchanged figure cannot just be dropped into an empty column, as the place value is lost. In this example, exchanging from the tenths, means that there will be ten hundredths, not one hundredth.