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3 Place value, ordering and rounding

! ere are hundreds of di"erent languages in use in the world today. Key words
However, all over the world people write numbers in the same way. Make sure you learn and
Everyone uses the decimal system to write numbers. understand these key words:

!e decimal system is a universal language. Why is that? jottings

One system that was used in the past is Roman numerals. significant figures

2000 years ago the Romans used letters to represent numbers. BIDMAS
You can still see them on clock faces and carvings. order of operations

!eir use continued in Europe for over 1000 years. Here are some examples.
Roman III VII IX XX C MCMXXX S
Decimal 3 7 9 20 100 1930 0.5

Here are some calculations, multiplying or dividing by 10 or 100, written with Roman numerals.
III × X = XXX V × C = D M ÷ C = X LV ÷ X = VS
Can you work out what D, M and L represent?

You can see that arithmetic with Roman numerals is very di$cult. You keep needing new letters.

!e decimal system uses place value. !at is why it only needs ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

!e symbols mean di"erent things in di"erent places. It makes arithmetic much easier.

Multiplying or dividing by 10 or 100 becomes very easy. You should be able to do these in your head.
7 × 10 = …… 2.4 × 100 = …… 6.3 ÷ 10 = . . . . . 45 ÷ 100 = . . . . .
You should be able to multiply or divide by 0.1 or 0.01 as well.
7 × 0.1 = …… 2.4 × 0.01 = …… 6.3 ÷ 0.1 = . . . . . 45 ÷ 0.01 = . . . . .

t !e decimal system was %rst developed in India.

t It was adopted by Persian and Arab mathematicians in the 9th century.
t It was introduced into Europe about 1000 years ago.
t At %rst it was banned in some European cities. People did not understand it

and thought they were being cheated.

Check: here are the answers to the questions: 70; 240; 0.63; 0.45; 0.7; 0.024; 63; 4500
In this unit you will learn how to multiply and divide decimals mentally. You will also learn how to
multiply and divide numbers by powers of 10, round numbers to a given number of decimal places and

signi%cant %gures, and make sure you use the correct order of operations.
3 Place value, ordering and rounding 23