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ARITHMETIC is the science which treats of numbers of the mode of expressing them-of the manner of computing by them-and of the various uses to which they are applied in the practical business of life.
The number one is called unity; and an integer, or whole number, is a collection of ones, unities, or units.
The figures, 1, 2, 3, 4, 5, 6, 7, 8, 9, denote, respectively, the numbers one, two, three, four, five, six, seven, eight, nine; the figure O, called zero or a cypher, expresses nought or nothing; but by means of these figures, which are called the ten digits, or more commonly the nine digits and zero, any number whatever can be expressed. This is effected thus :
A figure standing by itself, or on the right hand of other figures, has its own proper value, expressing so many units; A figure standing in the second place from the right is considered to express so many tens of units;
In the third place, so many tens of tens, or hundreds of units;
In the fourth place, so many tens of hundreds, or thousands of units, &c., according to the following Table, called
and so on to trillions, quadrillions, &c. if necessary.
Notation is the art of expressing any given number by these figures; Numeration the art of reading them, when so expressed.
N.B. Examples in Notation and Numeration may be obtained from those given in Addition and Subtraction.
The Romans used I for 1, V for 5, X for 10, L for 50, C for 100, D or I for 500, M or CIO for 1000.
When any character was followed by one of less or equal value, the expression denoted the sum of their simple values; but when preceded by one of less value, the difference; thus III stood for 3, IV for 4, and VI for 6, XL for 40, and LXX for 70, &c.
Every annexed to I, and every C and its value tenfold; thus I
joined to CIO, increased
stood for 5000, CCIƆ for 10,000, &c.
A line drawn over a character increased its value a thousand-fold; thus V stood for 5000, C for 100,000.
The following signs are also made use of in Arithmetic : +(plus) shows that the number before which it stands is to be added;
(minus) that the number before which it stands is to be subtracted;
× (into) that the numbers between which it stands are to be multiplied;
(by) that the number which stands before it is to be divided by the one which follows; and
(equal) that the numbers between which it stands are equal to each other.
-When any numbers are taken together, or added, the resulting number is called their sum.
Ex. Add 94163 21954
In order to add whole numbers together, we first place them under one another, with their units-figures in the same vertical line; we then add these figures thus, 5 and 7 are 12, and 3 are 15, and 2 are 17, and 4 are 21, and 3 are 24, i. e. 24 units, or 2 tens and 4 units; we set the 4 under the units-figures, to be the units-figure of the result, and carry the 2 tens to be added to the second or tens column; adding