ARITHMETIC. ARITHMETIC is the art of computing by numbers. Its leading rules are Addition, Subtraction, Multiplication, and Division. NOTATION AND NUMERATION. NOTATION is the method of expressing numbers. NUMERATION is the art of reading or writing any proposed number. The characters used in this science are called digits or figures, as follows:- It appears that each figure, when taken separately, expresses only so many units or ones; but by composition any number may be expressed, as may be seen from the following table, A 3 2 1 9 8 7 6 5 4 3 2 1 2 1980 6 5 0 3 20 8 7 4 5 6 7 8 3 1 2 3 4 5 6 7 3 4 5 6 7 8 6 4 3 2 1 Hundreds of Thousands of Millions. Hundreds of Thousands. coco Hundreds. -Units. 4 3 2 1 1 Here we may observe, that in the first line the 1 stands in the units place, and denotes one. In the 2nd line, the 2 stands in the tenth's place, and denotes two tens or twenty; the 1 stands in the units' place, and denotes one; consequently, the 2nd line denotes twenty one. In the 3rd line, the 5 stands in the hundredth's place, and denotes five hundred; the 6 stands in the tenth's place, and denotes six tens or sixty; the 7 stands in the unit's place, and denotes seven; consequently, the whole line makes five hundred and sixty-seven. In the 4th line from the bottom, the 4 stands in the thousandth's place, and denotes four thousand; consequently, the the whole line denotes four thousand three hundred and twenty-one. In the 5th line, the 6 stands in the tens of thousandth's place, and denotes sixty thousand; therefore the whole line denotes sixty-four thousand, three hundred and twenty-one. In the 6th line, the 3 stands in the hundreds of thousandth's place, and denotes three hundred thousand; consequently, the whole line denotes three hundred and fortyfive thousand, six hundred and seventy-eight. The top line denotes three hundred and twenty-one thousand, nine hundred and eighty-seven millions, six hundred three hundred and twenty-one. and fifty-four thousand, 7 6 5 4 3 3 1 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 EXAMPLES FOR PRACTICE. Write down in figures the following numbers :— 1. Forty-seven. 2. Four hundred and thirty-seven. 3. Fifty-six thousand two hundred and four. 4. One thousand eight hundred and forty-two. 5. Five millions, one hundred and five thousand and twenty one. 6. Two hundred and fifty-four thousand, three hundred and twenty-one millions, five hundred and one thousand, four hundred and twenty-one. |