STANDARD

ARITHMETIC.

NOTATION AND NUMERATION.

1 A single thing is called a Unit.

2. A unit or a collection of units is a Number.

A number answers the question "how many?"

A number may be expressed by words or other characters,
viz. figures and letters.

3. The method of expressing numbers by figures or let-
ters is called Notation.

The method of expressing numbers by figures is called the Arabic
Notation, from the Arabs who first introduced it into Europe.

The method of expressing numbers by letters is called the Roman
Notation, because it was used by the ancient Romans.

4. The method of reading numbers expressed by figures
or letters is called Numeration.

THE ARABIC SYSTEM.

5. In counting a large number of objects, it is natural to
arrange them in equal groups. When the number of the
first groups becomes large they may be gathered into larger
groups, and these again into larger groups, and so on. By
general agreement the system of grouping by tens, called
the decimal system, has been adopted.

6. The Arabic system of notation, which is a decimal
system, employs ten figures to express numbers, viz.:

0 1 2 3 4 5 6 7 8 9
Naught One Two Three Four Five Six Seven Eight Nine
Naught is also called zero and cipher.

By combining these figures in accordance with certain
principles, any number can be expressed.

7. PRINCIPLE.

When figures are written side by side,

the one at the right expresses units, the next tens, and the next

hundreds.

EXERCISES.

8. Tell what each figure in the following expresses:

9. Figures in units' place express units of the first order;

those in tens' place, units of the second order; those in hun-

dreds' place, units of the third order; etc.

10. The units of the second order, or tens, are named ten,
twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety.

The suffix ty means ten. Thus forty means four tens.

11. The numbers between 1 ten and 2 tens are named
eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen,
eighteen, nineteen.

Thirteen means three and ten; fourteen, four and ten, etc.

12. The other numbers between 20 and 100 are read with-
out the word and between the tens and the units.

Thus, 35 is read thirty-five, not thirty and five.