Billions.

Millions

Period.

The other successive periods are called Quadrillion, Quintillion, Sextillion, Septillion, Octillion, etc. Commencing with the right figure, which is called units of the first order, or simple units, the orders of figures, or units, to the left, are called units of the second order, units of the third order, fourth, fifth, sixth, etc.

ENGLISH SYSTEM OF NUMERATION.

40. There is in use a system known as the English numeration, which gives to each period after thousands, six places, or figures, instead of three as given by the French numeration. Numbers are divided into periods, and enumerated and read by the English numeration as shown by the following

English Numeration Table.

Each period of the higher orders has also six places.

REMARK.-The English system of Numeration being of no practical value to pupils in the schools of the United States, it will not be hereafter referred to.

41. The Arabic method of notation is based upon the following

General Principles.-1. The removal of any figure one place toward the left multiplies its value by ten; two places, by one hundred; three places, by one thousand, etc.

2. The removal of any figure one place toward the right divides its value by ten; two places, by one hundred, etc.

3. A cipher placed after a significant figure multiplies it by ten; two ciphers so placed, multiplies it by one hundred, etc.

2. Five units of the first order and two units of the second order.

3. Eight units of the first order, three of the second, and one of the first. 4. Four units of the fourth order, nine of the third, and two of the second. 5. Two units of the fifth order, nine of the third, and seven of the first. 6. One unit of the sixth order, nine of the fourth, six of the second, and eight of the first.

7. Seven units of the seventh order and seven of the first.

8. Six units of the eighth order, four of the sixth, seven of the fourth, and one of the second.

9. One unit of the ninth order, two of the eighth, three of the seventh, four of the sixth, five of the fifth, six of the fourth, seven of the third, eight of the second, and nine of the first.

43. Express by figures the following numbers:

1. Sixty-four.

2. One hundred forty-eight.

3. One thousand four hundred six.

4. Twenty thousand twenty-one.

5. Three hundred sixty-five thousand.

6. Eighty million forty-two.

7. Ninety thousand nine hundred.

8. Fifty million fifty-one

9. Eighty-seven billion seven thousand twelve.

10. Ninety-seven million ninety-seven thousand ninety-seven.

11. Twenty-one million twenty-five.

12. Sixteen billion sixteen million sixteen.

13. Six hundred eighty-nine thousand nine hundred seven.

14. Nineteen billion five hundred forty-one million eleven thousand eleven. 15. Twenty-seven quintillion eighty-one quadrillion two trillion seven hundred sixty billion one million two.

44. Point off into periods, numerate, and read the following numbers:

45. Write in words and read the following numbers:

ROMAN NOTATION AND NUMERATION.

46. By combining, according to certain principles, the letters used in this method of writing numbers, any number can be expressed.

Principles.-1. Repeating a letter repeats its value.

Thus, I = one, II two, X =

=

ten, XX = twenty.

2. If a letter of any value is annexed to one of greater value, the sum of the two values is indicated; if a letter of any value is prefixed to one of greater value, the difference of their values is indicated.

Thus, XI denotes X + I

=

eleven, IX denotes X I = nine.

3. A dash placed over a letter multiplies its value by one thousand.

=

Thus, V = five, V= five thousand, CD four hundred, CD four hundred thousand, LXVII = sixty-seven, LXVII sixty-seven thousand.

=

48. Express by the Roman system the following numbers:

2. Five units of the first order and two units of the second order.

3. Eight units of the first order, three of the second, and one of the first. 4. Four units of the fourth order, nine of the third, and two of the second. 5. Two units of the fifth order, nine of the third, and seven of the first. 6. One unit of the sixth order, nine of the fourth, six of the second, and eight of the first.

7. Seven units of the seventh order and seven of the first.

8. Six units of the eighth order, four of the sixth, seven of the fourth, and one of the second.

9. One unit of the ninth order, two of the eighth, three of the seventh, four of the sixth, five of the fifth, six of the fourth, seven of the third, eight of the second, and nine of the first.

43. Express by figures the following numbers:

1. Sixty-four.

2. One hundred forty-eight.

3. One thousand four hundred six.

4. Twenty thousand twenty-one.

5. Three hundred sixty-five thousand.

6. Eighty million forty-two.

7. Ninety thousand nine hundred.

8. Fifty million fifty-one

9. Eighty-seven billion seven thousand twelve.

10. Ninety-seven million ninety-seven thousand ninety-seven.

11. Twenty-one million twenty-five.

12. Sixteen billion sixteen million sixteen.

13. Six hundred eighty-nine thousand nine hundred seven.

14. Nineteen billion five hundred forty-one million eleven thousand eleven. 15. Twenty-seven quintillion eighty-one quadrillion two trillion seven hundred. sixty billion one million two.

44. Point off into periods, numerate, and read the following numbers:

45. Write in words and read the following numbers: