©
Wendy Fortescue-Hubbard and H G Beere
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personal use. Permission is also granted for copies of this document to
be made for students' immediate use within a teaching context. No other
rights are granted.
Lorries
move, Belisha beacons do not – unless a lorry hits them!
In
this example, the numbers appear on the side of a lorry. The lorry can drive
up the hill or reverse down the hill. The Belisha beacon does not move; it
represents the decimal point.
The ‘units’ column in a number is always just to the left of the
Belisha beacon. As we move further to the left there are the ‘tens’
column, the ‘hundreds’, etc. Conversely, to the right of the Belisha
beacon are the ‘tenths’ column, the ‘hundredths’ column,
etc.
Of course, just like real numbers the only column that is always present is the units column. When you start the program there is a one showing in the units column. We do not see any other numbers. They are there, but they are just zeros and we do not need to show them to tell us that we have one in the units column.
If you press the ×10 button you will see the lorry move up the hill. Then a zero appears between the one and the Belisha beacon. The number looks like a number ten – it is the number ten! This time we need the zero to let us know that the ‘1’ is in the tens column and means that there is one lot of ten and no units. If we did not put in the zero, it would look like a one, with a large space between it and the decimal point (the Belisha beacon).
What number would you get if you started with 1.1 and multiplied it by 10? To find out just press the ‘change value’ button and enter 1.1in the box. Press the ‘finished’ button when you are ready.
Try multiplying and dividing by other powers of ten and see what happens
to the lorry and the numbers. When some buttons turn grey it is just to stop
the numbers falling off the lorry and looking silly – in real life you
can multiply or divide by ten forever.