PRINCIPLES.

1. Ten units of any order make one unit of the

next higher order.

2. The removal of a figure one place to the left multiplies its value by ten.

3. The removal of a figure one place to the right divides its value by ten.

4. O is used to give place and value to the significant figures.

NOTE.-Let the pupil use a digit to illustrate the above principles.

3. The number next above 999 is called one thousand (1000), the 1 being a unit of the fourth order.

The fourth, fifth, and sixth orders complete a second period, called the period of thousands.

The seventh, eighth, and ninth orders form the period of millions.

The tenth, eleventh, and twelfth orders form the period of billions. Following billions are the periods of trillions, quadrillions, quintillions, etc.

4. Each period has units, tens, and hundreds of its

own.

5. Since ten units make one ten, and ten tens make one hundred, and ten hundreds make one thousand, and so on, the Arabic system of notation is called the decimal system. (Latin, decem, ten.)

6. The decimal system of notation is best set forth by means of a table.

NUMBER.

5 6, 920, 74 1, 65 8, 32 4, 506

This number, as analyzed by the table, is to be read thus: Fifty-six quadrillion, nine hundred twenty trillion, seven hundred forty-one billion, six hundred fifty-eight million, three hundred twenty-four thousand, five hundred six.

7. Notice the following features of the number in the table:

1. The periods of the number are set off by

commas.

2. All the periods have three digits except the

sixth.

3. In reading, the name of the first period (units)

is omitted.

4. The absence of significant figures is indicated

by 0.

NOTE.-A whole period may be indicated by three ciphers.

Millions.

Thousands.

Units.

1. Units.

9. Give the number of the following periods:

Quadrillions. Billions.

NOTE.-Observe that the first, fourth, seventh, tenth, thirteenth, and sixteenth orders name the periods to which they respectively belong.

11. Give the names of the following periods and orders:

9. 466214. 19. 7932468412. 29. 61314151617.

10. 664536. 20. 83749275867. 30. 618192021222. 31. 655256234625499844.

Analyze and read the first number, 5056.

Process.

5,056

Analysis.

Pointing off, we find there are two periods: thousands and units;—in the higher period, 5 thousands; in the other, O hundreds, 5 tens, 6 units. Hence, the number is read Five thousand fifty-six.

Analyze and read the eleventh number, 7385062.

Process.

7,385,062

Analysis.

Pointing off, we find there are three periods: millions, thousands, units. Beginning with the highest period and reading, we have Seven million three hundred eighty-five thousand sixty-two.

In like manner analyze and read each of the numbers in the first column.

Brief directions are:

1. Copy the number.

2. Beginning at the right, point off.

3. Beginning at the left, read.

4. Omit the last name, units.

14. Write in Arabic numerals thirty-six million twentynine thousand fifty.

Process.

3

2

1

m. th. u.

...

36,029,050

Explanation.

Since there are three periods,-millions, thousands, units,-we write three dots for each to indicate the number of places to be filled. We place 36 in the third period, 29 in the second, and 50 in the first. The places remaining unoccupied we fill with ciphers, and have 36,029,050.

Brief directions are:

1. Ascertain the number of periods and orders.

2. Beginning at the left, write the significant figures of each period, filling vacant places with ciphers.