STANDARD ARITHMETIC

CHAPTER I

NOTATION AND NUMERATION

INTEGRAL AND DECIMAL

1. The standards by which we count or measure are called units.

2. Numbers show how many units are expressed. In 5, 9, 25, 36, etc., the unit is 1.

In 2 bushels, 8 bushels, 15 bushels, etc., the unit is 1 bushel.

1

In 4 feet, 9 feet, 36 feet, etc., the unit is 1 foot. In 3 square feet, 6 square feet, etc., the unit is square foot.

3. Notation is the method of writing numbers.

4. The Arabic notation uses the figures:

5. The Roman notation used the letters, I, V,

6. Numbers are written in words when they are very important, as the numbers thus written are not so easily changed.

In writing in the amount on a business paper, we write, one hundred fifty dollars, instead of $150. The figures 150 might be easily changed to 750.

7. Numeration is the method of reading numbers. 2425 is read, two thousand, four hundred twenty-five.

8. In the use of the telephone and in calling numbers to others, we often name the figures in order, calling 2, 4, 2, 5 for 2425.

THE ARABIC SYSTEM

9. The Arabic system, which enables us to express all numbers, no matter how large, by the use of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, is a system of grouping by tens, called the decimal system, and is the one in common use.

10. In writing whole numbers, the units are expressed by the right-hand figure, each figure space at the left having ten times the value of its next right-hand figure space. In 33 the right-hand figure 3 expresses 3 units; but the 3 in the next place expresses ten times 3, or 30 units. In 433, the 4 expresses 10 x 10 x 4, or 400 units. 433 expresses 400 units, 30 units, and 3 units united into one expression, which we have learned to understand.

11. To read large numbers easily, we begin at units' place and group the figures into families or periods, and then give each period its family name as we read the number.

12. The names of these periods or families, in order from units' place toward the left, are; units, thousands, millions, billions, etc.

In writing large numbers so that they may easily be read, we separate them into periods by use of

commas.

We write 344487164 for reading, 344,487,164, and read it period by period; 344 million, 487 thousand, 164.

CAUTION. Do not separate numbers into periods while using them in computation. The comma which is used to separate periods is so nearly like the decimal point which is used to locate units' place, that it may be mistaken for it, if hastily made and used during computation.

13. Copy, point off into periods, and read aloud: 1. 34576, 453260, 432789, 40032, 435602, 435789.

2. 340678, 4023053, 8976420, 45320678,

45320679.

14. In writing numbers in figures when you see them written in words or hear them read, write each period as if it stood alone, then place the comma and write the next period.

In writing fifteen thousand, four hundred seven in figures, we write 15 as if it stood alone, place the comma, then write 407. We have written 15,407, which is correct.

In writing thirty-five thousand, we write 35 as if it stood alone, place the comma, and as there are no units fill out the places with ciphers, thus, 35,000.

The ciphers, while they have no value of themselves, must be used to show the proper place for the other figures.

1, 10, 100, 1000, 10000, are very different numbers, as the ciphers used have pushed the 1 farther from units' place each time, and multiplied its value by ten each step it is moved to the left.

15. The key to the Arabic system is the units' place. The value of each figure in a number depends upon its distance from units' place.

16. Write in figures the following numbers: 1. Ninety-four thousand, six hundred fifty-five. 2. Eighty-four thousand, nine hundred seventyfive.

3. Two hundred eighteen thousand, five hundred sixty-seven.