Three units of the second order, five of the first order. Five units of the second order, seven of the first order. Seven units of the first order, nine of the second order. Write all numbers below twenty.

Write all numbers between twenty and forty.

Write all numbers between fifty and seventy.

14. In reading numbers expressed by three figures, the tens are read after the hundreds, and the units after the tens, without the word and.

Thus, 346 is read three hundred forty-six.

Five units of the third order, two of the second, three of the first.

Two units of the third order, two of the second, two of the first.

Four units of the third order, four of the second, four of the first.

16. From the previous examples the following general principle is deduced:

PRINCIPLE. The representative value of a figure is increased ten-fold by each removal one place to the left, and decreased ten-fold by each removal one place to the right.

17. In writing and reading numbers, the figures are separated into groups of three figures each, called periods. These periods contain the hundreds, tens, and units of each denomination.

18. The following table illustrates the system of notation :

ORDERS.

HUNDREDS

N TENS

O UNITS

O HUNDREDS

TENS

W UNITS
N HUNDREDS

O HUNDREDS
A TENS

UNITS

W HUNDREDS
∞ TENS
01 UNITS

∞ HUNDREDS O TENS

UNITS

25, 673, 210, 040, 385, 861

The number is read twenty-five quadrillion, six hundred seventy-three trillion, two hundred ten billion, forty million, three hundred eighty-five thousand, eight hundred sixty-one.

1. Each period, except the one at the left, must contain three figures 2. The periods are separated from each other by commas.

3. In reading numbers the name of units' period is omitted. 4. The periods above quadrillions in their order are quintillions, sextillions, septillions, octillions, nonillions, decillions, etc.

RULE FOR NUMERATION.

·Beginning at the right, sepa

rate the numbers into periods of three figures each.

Beginning at the left, read each period as if it stood alone,

adding its name.

EXERCISES.

19. Copy, point off into periods, and read:

1. Twenty-nine billion, ninety-five thousand, forty-five.

EXPLANATION. — We first write the numbers of the highest denomination, following them with a comma. After that we write the numbers of the next lower denomination, or mil29,000,095,045. lions, but since there are none, we fill the period with ciphers, and write a comma after them. This is followed by 095 in the next lower period, and 045 in the last, the figure 0 being placed before the significant figures to make the periods complete.

RULE FOR NOTATION. ·Begin at the left and write the hundreds, tens, and units of each period in their proper order, putting ciphers in all vacant places and periods.

While writing, separate each period by a comma from the one that follows it.

Write in figures:

2. Twenty-five thousand, eight hundred fourteen.

3. Thirty-nine thousand, seven hundred twenty-four. 4. Ninety-four thousand, six hundred fifty-five.

5. Twenty-nine thousand, five hundred eighty-five. Eight thousand, six hundred five.

6. Forty-six thousand, eight hundred twenty. Forty thousand, eight hundred nineteen.

7. Eighty-four thousand, nine hundred four. Fifteen thousand, nine. Eight thousand, four hundred.

8. Nineteen thousand, nine hundred nine. Four thousand, eight. Eighteen thousand, seven hundred.

9. Twenty-four thousand, two hundred eight. Twenty thousand. Thirty thousand, seven hundred.

10. Fifteen thousand, four hundred seven. Four thousand, seven. Twenty thousand, two hundred.

11. Thirty-seven thousand, nine hundred. Thirty thousand, thirty.. One hundred thousand, eight hundred five.

12. Fifty-five thousand, five hundred five. Five thousand, five. Thirty thousand, nine hundred nine.

13. Forty-eight thousand, fifty-five. Forty thousand, eight. Seventeen thousand, seven hundred three.

14. Sixty-six thousand, eighty. Fifty-five thousand, nine. Fifty thousand, three hundred eighty-five.

15. Eighty-five thousand, eight hundred eight. Eightyeight thousand. Eight thousand, eight hundred eight. 16. Thirty thousand, three hundred thirty-five. Twenty thousand, nine. Ninety thousand, two hundred eight.

17. Two hundred eighteen thousand, five hundred sixtyseven. Eighty thousand, seven hundred twenty.