13.

TABLE OF ARABIC NOTATION

1 2 7, 34 6, 2 0 8, 6 3 5, 4 0 9.239 107

Observe in the above table that

a. The decimal point (.) is placed between units' and tenths' places. Figures at the left of the decimal point express integers, and figures at the right of the decimal point express decimal fractions.

b. The different orders of units are numbered from the decimal point both to the right and to the left.

c. The values of the different orders of units increase uniformly from right to left and decrease uniformly from left to right in a tenfold ratio, throughout the integer and the decimal.

d. The name of each period is the same as that of the righthand place in that period.

e. Commas are used to separate the periods, for convenience in reading.

14. A number that is composed of an integer and a decimal is called a mixed decimal; e.g. 2.5, 31.242, 600.00006.

15. Naming the places of figures and reading numbers is numeration; e.g., to numerate the number .40236, we should say, tenths, hundredths, thousandths, ten-thousandths, hundredthousandths- forty thousand two hundred thirty-six, hundred-thousandths.

16. In reading numbers, the word and should not be used except between the integer and the decimal of a mixed decimal, or between the integer and the fraction of a mixed number; e.g. 30,245 is read, thirty thousand two hundred forty-five; .328 is read, three hundred twenty-eight thousandths; 30,245.328 is read, thirty thousand two hundred forty-five and three hundred twenty-eight thousandths.

17. Read the following integers and write them in words:

18. Read the following decimals and write them in words:

19. Read the following mixed decimals and write them in

20. Express the following numbers in figures:
1. Two hundred thousand, two hundred.
2. Twelve thousand, and two thousandths.
3. Eighty-eight thousand, and three hundredths.

4. One hundred, and one hundred thousandths.

5. One hundred thousand, and one hundred-thousandth. 6. Three thousand one hundred-thousandths.

7. Eight thousand, and eight thousandths.

8. Five billion, sixty thousand, two hundred.

9. Three hundred six million six.

10. Forty-eight thousand two hundred, and two hundredthousandths.

11. Three hundred seventy-five thousand sixty, and four hundred ten thousandths.

12. Seventy thousand four hundred, and four hundred tenthousandths.

13. Sixty thousand fifty, and sixty-nine ten-thousandths.

14. Ninety-one, and ninety-one thousandths.

15. Two thousand three hundred one, hundred-thousandths. 16. Five hundred eighteen, and five hundred eighteen tenthousandths.

17. Thirty-nine thousand four millionths.

18. Two hundred two thousandths.

19. Two hundred, and two thousandths. 20. Two and two hundred thousandths. 21. Two and two hundred-thousandths.

22. Six hundred six thousand.

23. Six hundred six thousandths.

24. Six hundred, and six thousandths.

25. Six hundred, and six hundred thousandths.

26. Six hundred, and six hundred-thousands.

ROMAN NOTATION

21. Expressing numbers by means of letters is Roman notation.

For many years the Roman system of notation was commonly used in Europe. The ancient Greeks also had a system of notation which employed the letters of the Greek alphabet. Both of these systems were awkward, and of little use in making computations.

The Arabic numerals were used first in India. The figure 0 was lacking until about the fifth century. Its introduction added greatly to the usefulness of the system.

Arabic notation was first used in Europe about the twelfth century, having been brought there by the Arabs. It is now the prevailing system of notation throughout the civilized world.

22. The Roman system of notation employs the following seven capital letters in expressing numbers:

I (1), V (5), X (10), L (50), C (100), D (500), M (1000).

In combining these letters, the following principles are observed:

a. Repeating a letter repeats its value; e.g.

X=10, XX=20, XXX = 30.

b. When a letter follows one of greater value, its value is added to the greater value; e.g. C 100, L= 50, CL = 150.

=

C. When a letter precedes one of greater value, its value is subtracted from the greater value; e.g. C=100, X = 10, XC = 90.

d. When a letter is placed between two letters of greater value, its value is subtracted from the sum of the two greater values; e.g. C=100, X= 10, L= 50, CXL= 140.

e. A bar placed over a letter multiplies its value by 1000; e.g. XC= 90, XC = 90,000.

23. Read the following numbers and express them in Arabic numerals: