ARABIC NOTATION.

15. The Arabic System of Notation expresses numbers by means of characters called figures. These figures are 1 (one), 2 (two), 3 (three), 4 (four), 5 (five), 6 (six), 7 (seven), 8 (eight), 9 (nine). Sometimes these figures are called digits.

16. Grouping Numbers. - Nine is the largest number that can be expressed by a single figure. To express larger numbers, two or more figures must be combined. But in order to combine these figures in a systematic way, numbers must be thought of as in groups. The system of grouping employed in the Arabic notation is by tens. Ten ones are grouped into a larger collection and called one ten. Ten is one of a new kind, and the figure 1 is used to express it. This is done by putting the 1 in a new place; that is, the 1 is removed one place to the left.

17. The Decimal Point.- But, in order that we may know that the 1 is in the second place to the left, there must be something to count from. For this purpose a dot is used, and it is called a decimal point.

18. The Zero.- Further, in order to prevent any mistake as to the place of the 1 with reference to the decimal point, a character is needed to put in the first place whenever just one ten or some exact number of tens are written. The character 0 is used, and it is called zero. Hence, 10 expresses ten written in figures.

19. Writing Numbers.- Any number of tens from one to nine can be expressed by writing the figure whose shape denotes the number of tens to be expressed, in the second place to the left of the decimal point.

EXERCISES.

20. Write in figures: Two tens, three tens, four tens, five tens, six tens, seven tens, eight tens, nine tens.

Two tens (20) is read twenty, three tens (30) thirty, four tens (40) forty, etc.

Write in figures: Two tens and three ones, three tens and four ones, four tens and four ones, five tens and three ones, six tens and seven ones, seven tens and six ones, eight tens and five ones, nine tens and eight

ones.

21. Writing Larger Numbers.- Nine tens and nine ones (99) is the largest number that can be expressed by two figures. The next higher number is ten tens. These are grouped into a larger group, and called one hundred. This is one of still another kind, and the figure 1 is used to express it. This is done by putting the 1 yet another place to the left, or in the third place, thus-100. Any number of hundreds from one to nine can be expressed by writing the figure whose shape denotes the number of hundreds to be expressed, in the third place to the left of the decimal point. Use zeros if no lower denominations are given.

EXERCISES.

22. Write in figures: Two hundreds, three hundreds, four hundreds, five hundreds, six hundreds, seven hundreds, eight hundreds, nine hundreds.

Write in figures: Two hundreds three tens, three hundreds two tens four ones, four hundreds one ten three ones, five hundreds five tens, six hundreds four tens seven ones, seven hundreds two ones, eight hundreds six ones, nine hundreds nine tens nine ones.

23. Writing Numbers Greater than One Thousand.- Nine hundreds nine tens and nine ones (999) is the largest number that can be expressed by three figures. The next higher number is ten hundreds. These are put into one group and called one thousand. This is expressed in figures by putting the 1 in the fourth place to the left of the decimal point. In the same way thousands are grouped into tens of thousands, and tens of thousands into hundreds of thousands, and so on. Thus, the Arabic system of notation is a decimal system (decem means ten). Ten units of any order always make one unit of the next higher order.

24. Principles.-I. ward the left makes its before.

Moving

Moving a figure one place tovalue ten times what it was

II. A zero is used to fill a place that would otherwise be vacant between some figure and the decimal point.

The zero has no other use in arithmetic. Annexing zeros does not " multiply" or in any way change the value of figures. The value is changed by the change of place with respect to the decimal point; the annexing of zeros may show that the place has been changed.

III. Figures have two kinds of value, viz., a shapevalue and a place-value.

The shape-value shows the number of ones in the number expressed. It answers the question, "How many?" The place-value determines the kind of ones, as units, tens, tenths, etc. It answers the question, "What kind?"

The place-value is determined by the position of the figure with reference to the decimal point.

Instead of shape-value and place-value, it is common to say simple and local value.

PERIODS,

12,500,731,049,020,860

Sixth. Fifth. Fourth. Third. Second. First.

The periods above quadrillions, in their order, are: Quintillions, sextillions, septillions, octillions, nonillions, decillions, undecillions, duodecillions, tredecillions, quatuordecillions, quindecillions, sexdecillions, septendecillions, octodecillions, novendecillions, vigintillions.

Observe the list of the names of periods as just given. Write the list down, beginning with trillions, and cut off the termination "illions" from each word. What remains of each name signifies a number; these numbers go on in regular order from three to twenty. Thus, tr=3, quadr=4, quint=5, sext=6, etc. (The first three names are omitted, as their significance is not so clear.)

Now "trillions" is the name of the fifth period, “quadrillions” of the sixth, “quintillions" of the seventh, etc. In other words— The number of the period is always greater by two than the number signified by the first part of its name.

27. To Write a Number in Figures.-Begin at the left hand and fill each period in order, using zeros where there is no number to express.