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ARITHMETIC.

BY

REV. C. ELSEE, M.A.,

LATE FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE;
ASSISTANT-MASTER AT RUGBY.

INTENDED FOR THE USE OF RUGBY SCHOOL.

LONDON:

BELL & DALDY, 186, FLEET STREET,
AND 6, YORK STREET, COVENT GARDEN.

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LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD street,

AND CHARING CROSS.

ARITHMETIC.

CHAPTER I.

DEFINITIONS AND SIMPLE RULES.

1.—ARITHMETIC is the science which treats of numbers.

Numbers are expressed in Arithmetic by means of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; by the use and proper arrangement of which any number whatever may be represented.

The above figures are termed digits.

2.-(a). The art of expressing a number by means of digits is called notation: and the common system, in which the expression of numbers is founded on their relations to ten, ten tens, &c., is called the decimal system, or decimal scale of notation.

A single object of any kind is called a unit of that kind, as one book, one pound, one hour, &c.

A number of units less than ten is represented by one of the above digits. A number as high as ten, but below a hundred (i. e. ten tens), is written with two digits, of which the left hand one expresses the number of tens, and the right hand one the number of units additional, in the number. Thus seventy-five, i. e. 7 tens and 5 units, expressed in figures would be 75. A number as high as a hundred and below a thousand (i. e. ten hundreds) is written with three digits; the first, or left hand one, expressing the number of hundreds contained in the given number, the second the number of tens besides, and the third the remaining number of units. Thus three hundred and forty-six, i. e. 3 hundreds, 4 tens, and 6 units, would be 346. So, for a thousand or

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above, four digits must be used; for ten thousand, five digits; &c.

(b). Numeration is the converse of notation, and is the art of expressing in words a number given in figures.

The explanation given above will sufficiently indicate the method of doing this. It will be noticed that whatever the number of digits in a number, the last digit on the right always represents units; the last but one, tens; the next, hundreds; &c.

The following table may be useful:

3 4 7

6

5 9

Tens.
Hundreds.

Units.

∞ Thousands.

Tens of thousands.
Hundreds of thousands.

• Millions.

Tens of millions.

Hundreds of thousands of millions.

Tens of thousands of millions.

Thousands of millions.

Hundreds of millions.

+ Billions.

Tens of billions.

Hundreds of billions.

&c.

Ex. (1) Three hundred and twenty-five thousand, two

hundred and fifty-seven, would be written in figures as

325257.

Ex. (2) Twenty-eight millions seven hundred and fortyfour thousand one hundred and sixty-nine, would be 28744169.

Ex. (3) Ten thousand three hundred and eighty, would be 10380.

Ex. (4) Five hundred thousand three hundred and one. Here there are no tens of thousands, no units of thousands, and no tens; each of these places must be supplied by a o; and we shall have 500301.

ARITHMETIC.

CHAPTER I.

DEFINITIONS AND SIMPLE RULES.

1.-ARITHMETIC is the science which treats of numbers.

Numbers are expressed in Arithmetic by means of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; by the use and proper arrangement of which any number whatever may be represented.

The above figures are termed digits.

2.-(a). The art of expressing a number by means of digits is called notation: and the common system, in which the expression of numbers is founded on their relations to ten, ten tens, &c., is called the decimal system, or decimal scale of notation.

A single object of any kind is called a unit of that kind, as one book, one pound, one hour, &c.

A number of units less than ten is represented by one of the above digits. A number as high as ten, but below a hundred (i. e. ten tens), is written with two digits, of which the left hand one expresses the number of tens, and the right hand one the number of units additional, in the number. Thus seventy-five, i. e. 7 tens and 5 units, expressed in figures would be 75. A number as high as a hundred and below a thousand (i. e. ten hundreds) is written with three digits; the first, or left hand one, expressing the number of hundreds contained in the given number, the second the number of tens besides, and the third the remaining number of units. Thus three hundred and forty-six, i. e. 3 hundreds, 4 tens, and 6 units, would be 346. So, for a thousand or

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