Chocolate bar with ten pieces
On this page there are several questions ~ every one is dealing with decimals. There will be more on decimals ~ later ~ but it is important to understand this type of study first of all.
Decimals are small bits of something. The something depends on what you are talking about - normally the something is the whole thing. An example might be the whole class ~ or everyone in the school ~ or a whole orange ~ or a complete pizza. The small bits in decimals for this page will always be when the whole things is sliced into ten pieces ~ mathematicians call such slices tenths. (Later it will be even smaller bits ~ when the whole thing is divided into a hundred bits and we call them hundredths. The decimal system works in jumps of ten, or a hundred, or a thousand.
This bar of chocolate has ten pieces. I could divide it ~ fairly ~ equally ~ amongst ten people. Each person would get one tenth. This could be written as a fraction ~ 1/10 ~ or as a decimal •1. If I was reading that I would say 'Point one'. The point is just a dot ~ called the decimal point ~ and then a digit.
As another example ~ 3/10 is 'point three' or •3. There is a danger that a small dot might go unnoticed amongst a page of writing words and numbers. So people write 0·3 or 0·1 and they say 'nought point three' ~ or Zero point one' ~or other ways that mean the same thing ~ 'The gangsters are now approaching the road block and are zero decimal seven kilometres away'.. The extra reference to the 0 reminds everyone that there is a decimal point to be noticed.
There is a big difference between someone saying 'Would you like 0·3 chocolate bars or 3·0 chocolate bars'. I know which I would rather have.
In the picture above I have covered some pieces of the same chocolate bar with paper. How may pieces have I hidden? How many pieces have I left showing?
If you are thinking the answers ~ or talking ~ you will ~ I hope ~ have said 'Three pieces' and 'Seven pieces'. You may also have thought something along the lines of 'Three plus seven is ten ~ that seems a good confirmation'.
My question ~ for the same picture ~ might be 'What fraction of the whole bar has been covered?' and 'What fraction of the whole bar has been left showing?'
Your replies would be almost the same ~ 'Three tenths' and 'Seven tenths'. Since there are ten pieces in the whole bar three pieces can be stated as three tenths. It could also be said as 'Zero point three of the bar' or written as 0·3.
As a diagram I could have made the picture look like this ~
~ or even like this ~
