Early Decimal Practice

First decimal place

This page is about working to one decimal place ~ which means single digit decimals. Working to one decimal place means counting up how many tenths of something. A tenth of something is when that thing is divided ~ shared ~ cut ~ sliced ~ chopped ~ into ten equal pieces. The thing can be anything. Maths teachers are keen to use things that look easy to cut into ten pieces ~ so that you can easily see what is happening. I have chosen a small bar of chocolate ~ because it is ready to be broken into ten pieces.

Small chocolate bar of ten pieces
Chocolate bar with ten pieces

Other examples might be a whole orange ~ or a complete pizza. It would be easy to divide a pot of jam into ten equal portions ~ but it would be a good idea to do that in a kitchen. It is not easy to for me to draw meaningful pictures of spoons of jam.

For the rest of this page I am thanking and drawing sketches of this chocolate bar ~ no more jam or pizzas here.

This bar of chocolate has ten pieces. I could divide it ~ fairly ~ equally ~ easily ~ 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 what I have just written I would say 'Point one'. The point is just a dot ~ called the decimal point

As another example ~ 3/10 is 'point three' or •3.

I have drawn the dot very large. It is much easier to draw a small dot ~ a bit like a full-stop. There is a danger that a small dot might go unnoticed amongst a page of writing words and numbers. It is good practice to emphasise that there is a dot by adding a zero to the left of it. The zero does not effect the maths ~ it nudges the eyes to see the decimal point. Everyone ~ all over the World ~ seems to be doing it that way. It must a be a good idea.

When people write 0·3 or 0·1 they have to say it in some other way such as ~ 'nought point three' ~ or Zero point one' ~ or maybe in 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 word 'zero' or 'nought' reminds everyone that there is a decimal point to be noticed.

The decimal point is important. 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.

Small chocolate bar puzzle
Chocolate bar with some hidden pieces

In the picture above I have covered some pieces of the same chocolate bar with paper. How many pieces have I hidden? How many pieces have I left showing?

If you are thinking the answers ~ or talking about them with someone ~ you will ~ I hope ~ have said 'Three pieces' and 'Seven pieces' as your answers to my questions above. You may also have thought something along the lines of 'Three plus seven is ten ~ that seems a good confirmation'. We will do more along those lines later.

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 ~

Small chocolate bar puzzle
Diagram of chocolate bar with three tenths ~ 3/10 ~ of the whole shaded

~ or even a less mouth-watering diagram looking like this ~

Fractions demonstrated
Diagram of something ~ with 3/10 gone ~
or ~ 'zero~point~three is missing'


Here is a new diagram ~

Fractions demonstrated
Diagram of part of something ~ how much is missing?

I hope you thought of one tenth missing ~ and maybe you also thought of zero~point~one of the whole as having gone.

Here are some more pictures and questions. Write down the answers in words or numbers ~ using the letters indicated to keep track of your work.

Fractions demonstrated
Diagram for question A

A What fraction of the whole shape is coloured brown?

Fractions demonstrated
Diagram for questions ~ B and C and D and E

B What fraction of the whole shape is coloured brown?

C What decimal of the whole shape is coloured brown?

D What fraction of the whole shape is missing?

E What decimal of the whole shape is missing?

Fractions demonstrated
Diagram for questions ~ F, G, H, J and K ~
there is no question I

Sometime people use other words that mean exactly the same things. If I do that I hope you will be able to work things out ~ nothing is changed apart from a word here and another word there.

F What fraction of the whole shape is coloured brown?

G What decimal fraction of the whole shape is coloured brown?

H What proportion of the whole shape ~ expressed as a fraction ~ is missing?

J Can you express your answer H in another way?

K Can you express the answer you gave for A in another way by using a single word that has not yet appeared on this page? If this question seems strange ~ or odd ~ or difficult ~ then leave it alone and do not worry about it.

You will have noticed the words decimal fraction were used. That is because decimals and fractions are very similar in lots of ways. From now onwards you will be able to think in a bi-lingual fashion.

Another point to mention ~ it sometimes causes a muddle for youngsters at first ~ is that the decimal point is often written as a full stop, especially in some other countries.

When writing money, some people say you should use a hyphen instead of a decimal point ~ but not if there could be confusion with the minus sign. I hope that soon it will become automatic for you to know that a tenth is the same as one tenth ~ and is the same as point one ~ and is the same as zero point one ~ and is the same as 1/10 ~ and is the same as 0·1.

Fractions demonstrated
Diagram for questions ~ L, M, N, P and Q ~
there is no question O

L What proportion of the whole shape is coloured brown ~ written as a fraction?

M What proportion of the whole shape is coloured brown ~ written as an different but equivalent fraction?

N What decimal fraction of the whole shape is coloured brown?

P What proportion of the whole shape ~ expressed as a fraction ~ is missing?

Q The answer to this question when added to the answer of question L equals exactly one whole or 1 or 1.0. Write down what you think the question is.

Fractions demonstrated
Diagram for questions ~ Q and R and S

Q Write down a question along the same lines as all the others ~ and provide the answer

R Same as question Q ~ but different in some way

S Same as question Q ~ but different from Q and R

Fractions demonstrated
Diagram for questions ~ T and U and V

T Write down a question along the same lines as all the others ~ and provide the answer

U As question T ~ but different in some way

V As question T ~ but different from T and U

You may have learned ~ at school ~ that 5/10 is the same as a 1/2 when using Equivalent Fractions. As a decimal it is 0·5. Surely you will now be able to remember that 1/2 equals 0·5 equals one half.

Medium fraction of a chocolate bar
V How much has gone?

Small fraction of a chocolate bar
W How much is left?

I could share a reward with you ~ but only 0.3 of the bar is left. I know where the rest went.



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Last updated 2021/02/06
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