1

As civilisations developed, spoken languages were written down using symbols. Symbols are letters and marks which represent sounds and ideas. Thus the words on this screen are symbols for spoken words. Numbers were also written down.

2

We use the word numerals for number symbols. For example, ٢ and 二 are the numerals for two in Arabic and Chinese. We use the numeral 2 for two.

3
### Tally system

The first numera1s were probably tally marks. People who looked after cattle made tally marks to represent the number of animals they had
The tally marks were scratched on stones or sometimes cut on sticks
We still use the tally systcm; it is very useful when counting a large number of objects. We usually group tally marks in fives; thus ///// ///// /// means three fives and two, or seventeen. Notice that in each group of five, the fifth tally is marked across the other four:

4
### Roman system

There were many ancient methods of writing numbers. The Roman systcm is still used today. The Romans used capital letters of the alphabet for numerals. In the Roman systcm Is stand for units, x's stand for tens and C's stand for hundreds. Other letters stand for 5's, 50's and 500's. The list below shows how the letters were used.
1 I
2 II
3 III
4 IIII or IV
5 V
6 VI
7 VII
8 VIII
9 VIIII or IX
10 X
20 XX
40 XL
50 L
60 LX
90 XC
100 C
400 CD
500 D
900 CM
1000 M

5
### Counting Board

The Roman systcm made it difficult to add and subtract numbers. Paper and pencil calculations took a long time. Traders and bankers used simple calculating machines. The counting board and the abacus were early examples of these.
A counting board was a block of stone or wood ruled in columns. Loose counters, stones or seeds were placed in the columns to show the value of the numbers in the columns (Fig. 1.2).
Counters in the right-hand column (U) represented units, counters in the next column (T)' represented tens, and so on.
Usually the columns were not labelled. Small crosses were used to mark every three columns. We still group digits in threes when writing large numbers, e.g. 6 452 308. It is easy to make a paper counting board

6
### The Abacus

The abacus is similar to the counting board. An abacus has wires and beads instead of columns and counters. The wires are mounted on a frame. To record numbers, the beads are moved from the top of the frame to the bottom.

o

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