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INTERMEDIATE

ARITHMETIC.

NOTATION AND NUMERATION.

1. A single thing is called a Unit.
Thus, one, a pencil, a tree, a quart, are units.
Units are also sometimes called ones.
2. A unit or a collection of units is called a Number.
A number answers the question “How many ?"

A number may be expressed by words, and represented by figures and letters.

3. The method of representing numbers by means of figures or letters is called Notation.

4. The method of reading numbers is called Numeration.

THE ARABIC NOTATION. 5. The method of representing numbers by means of figures is called the Arabic Notation.

It is called the Arabic Notation because the Arabs first introduced it into Europe.

6. In this notation ten figures are employed to represent numbers, viz. : FIGURES : O, 1, 2, 3, 4, 5, 6, 7, 8, 9. NAMES :

Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. Each of these, except naught, is called a significant figure. Naught is also called zero and cipher.

7. The number that is one more than nine is called Ten.

1 ten is called ten, and is written, 10.
2 tens are called twenty, and are written, 20.
3 tens are called thirty, and are written, 30.
4 tens are called forty, and are written, 40.
5 tens are called fifty, and are written, 50.
6 tens are called sixty, and are written, 60.
7 tens are called seventy, and are written, 70.
8 tens are called eighty, and are written, 80.

9 tens are called ninety, and are written, 90. The suffix ty means ten. Thus, forty means four tens; etc.

8. It will be observed that the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which standing alone represent units, are made to represent tens by writing 0, meaning zero units, after them. Thus, 50 means five tens and zero units, or five tens.

9. Instead of 0 any of the figures may be written in the right-hand place to represent units. Hence,

When two figures are written side by side, the one at the right represents units and the one at the left tens.

EXERCISES. 10. 1. In 25, what does the figure 2 represent? What does 5 represent? Read the number, beginning at the left.

2. In 72, what does 7 represent? What does 2 represent ? Read the number, beginning at the left.

3. In 38, what does 3 represent? What does 8 represent? Read the number, beginning at the left.

4. Tell what each figure represents in the following, and read each number, beginning at the left: 21 62 77 39 55

46
43 28 54 94 88 79
36 23 34 63 57 81
30 50

60
20

90

40

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