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and they relate to a wide range of subjects drawn from modern life and industries. The information they embody has been gathered from reliable sources. The prime object of the book, however, is not to convey information on extraneous topics, but to teach the processes of arithmetic in the best way possible. ... "

WILLIAM J. MILNE.

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PROGRESSIVE ARITHMETIC

THIRD BOOK

NOTATION AND NUMERATION

1. Any one thing is called a unit.
One, a book, a dollar, a gallon, are units.
2. A unit or a collection of units is called a number.

Numbers are represented by characters, as figures or letters, and are expressed by words.

3. Any method of representing numbers by characters is called notation.

The notation by figures, in common use among civilized nations, is the Arabic, named from the Arabs who first introduced it into Europe. It is sometimes called the Indian, or Hindu, notation because it originated in India.

For certain purposes we use a notation by letters called the Roman notation. It was named from the ancient Romans who used it.

4. Any method of naming, or reading, numbers represented by characters is called numeration.

The method in common use in America is known as the French numeration.

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 still larger groups, and so on.

The system of grouping that is most commonly used is that of grouping by tens, called the decimal system from the Latin word decem meaning ten.

In such a system 10 units make a group, 10 of these groups make a larger group. 10 of these larger groups make the next larger group, and so on.

6. The Arabic system of notation is a decimal system. It represents numbers by means of the following ten figures combined according to certain principles:

one two three four five six seven eight nine naught

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Naught is also called zero and cipher. It represents no value and is used to fill vacant places.

The other nine figures are called significant figures, because each represents a value.

7. In this system a group of ten is called one ten, written 10; a group of 10 tens is called one hundred, written 100; a group of 10 hundreds, one thousand, 1000; ete.

8. In the number 1111, the first 1 beginning at the right stands for 1 unit, the others in order toward the left for 1 ten, 1 hundred, and 1 thousand,

What does each 4 in 4444 represent? each 7 in 7777?

9. The decimal system may be extended indefinitely to the left or to the right. Before extending it to the right, a dot called the decimal point is placed after the figure that represents units.

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