ARITHMETIC. ARITHMETIC is the science of the use of numbers. The figures used are: 1 2 3 4 5 6 7 8 9 these are called the nine SIGNIFICANT DIGITS, and with these any number can be expressed by combining them with one another and with o (called zero or cipher). The old Roman way of expressing numbers with letters is never used now in Arithmetic. It is explained at the end of the book. See page 173. (1.) Notation. Expressing a number by means of figures is called NOTATION. The figures are placed in a line and each figure has a LOCAL VALUE according to its place in the line. In the first place (to the right) it stands for so many units. In the second place it stands for so many tens. hundreds, and by each move of one place further from the right its local value is increased tenfold. B Thus: 7 means 7 ones or units, 47 means 7 units and 4 tens; that is forty-seven. 847 means eight hundred and forty-seven. 2847 means two thousand eight hundred and forty-seven. The following table shows the local value which a figure has in each place up to the billions; the student can continue the table still farther if he pleases. Billions. Millions. Thousands. Units. 12th. 11th. 10th. 9th. 8th. 7th. 6th. 5th. 4th. 3rd. 2nd Ist. In this table the billions begin at the 10th place. This is the French or Continental system, and is now commonly adopted in England. According to the old English system the billions began at the 13th place, but the difference is not of much importance as such high numbers seldom occur in any calculations. From this table we form our RULE FOR NOTATION. Mark off divisions wide enough to hold three figures each these divisions are called PERIODS write over the first period write over the third period units millions billions |