1. Decimal Counting.-Many hundred years ago counting and computing were carried on by the use of fingers, pebbles, sticks, knots in ropes, and sand strewn upon stone tablets. Counting 10 units to make 1 ten, 10 tens to make 1 hundred, and so on, has likely arisen from finger counting. We even call our number symbols 1, 2, 3, etc., digits, which is also another name for fingers. A counting system based upon tens, as is ours, is called a decimal system.

2. Early Number Systems. Separate symbols were used for each number in the early number systems. In one such system 10 was A, 20 was A, 100 was, and 200 was . Symbols written one after the other were usually added together. Thus, 50 would be AAA. How?

1

3. Roman Number System.-The Roman number system was one of the early systems and is still used to-day for some things. In this I, V, X, L, C, D, M stand for 1, 5, 10, 50, 100, 500, 1000. A dash over any symbol multiplies it by 1000. Thus V is 5000. Any symbol following one of the same or of larger value is added to the one before it. Any symbol preceding one of larger value is taken from the one following it. In this way are made 4 (IV), 9 (IX), 40 (XL), 90 (XC), and also 400, 900, 4000, 9000. Express these last four numbers in Roman numerals.

4. Hindu-Arabic Number System.-Over 1000 years ago the Hindus, in far away India, invented our present simple number system. They used 9 numerals as we do the 1, 2, 3, etc., but these were slightly different in form. These numerals-digits-they combined into numbers based upon the decimal idea just as is done to-day. Each of the digits, 2, 4, and 8, in the number 248 has a definite value. Each digit also has a value due to its position in the number. This is called its place value. number as 248. What other numbers can be made from the digits 2, 4, and 8? Which is the largest? Which is the smallest ?

Thus, 482 is not the same

At the time that the Hindus invented their number system the Arabs were the chief merchants of the world and carried goods from one country to another. In trading with the Hindus, the Arabs learned this simple number system, which they adopted. As they traded with the people of Europe and of Africa, they brought the Hindu system of numbers into these countries. The Arabs had nothing to do with inventing this simple number system, but because they brought it into Europe it has incorrectly been called the Arabic number system.

5. Fractions in the Hindu Number System. In 1548 Simon Stevin of Flanders invented decimal fractions which are an extension of the Hindu number system to fractions. In 387.42 the 4 is one-tenth of what it would be where the 7 is; the 2 is one-tenth of what it would be where the 4 is and so on. In reading numbers use and for the decimal point but at no other time.

EXERCISES

1. Read the following: IX; XI; XXIV; XL; LX; LXV; CL; MC; CM; CMXIV; MCMXVIII; MCMXX; MCMXIX; X; L.

2. Express the following in Roman numerals: 15; 20; 25; 75; 205; 410; 1905; 1050; 1910; 1918; 1924; 5000; 6000.

3. What is the value of each of the digits in 4444?

4. Separate each of the following numbers into periods of three digits and read:

in 3.465; in 5.307; in 34.005; in 2.4506.

6. Read the following decimals: 304.56; 2304.245; 3.4506; 30.2054; 19.0045; 0.00452; 1.0504; 305.0072; 0.00025; 1.00503; 0.02056; 5.000035; 0.030502.

7. Write the following numbers: one hundred thirtyfive and two tenths; seventy-four and twenty-six hundredths; one thousand fifteen and thirty-four thousandths; ninety and one hundred eight tens-of-thousandths; forty hundredths.

6. Reading and Writing Numbers. When writing numbers in words be careful to use the hyphen in such numbers as twenty-five, sixty-four, and so on. Use and only where the decimal point comes. Thus, thirty-seven dollars and twenty-nine cents.

Business and scientific men read such numbers as 2453.78, "twenty-four, fifty-three, point, seventy-eight"; 63.07, "sixty-three, point, oh, seven." As a telephone number, 4526 would be called "four, five, two, six."

EXERCISES

1. Write the following numbers in words: 35; 83; 70; 165; 235; 5,362; 306; 5,073; 7,004; 2,049; 8,000; 34,007. Read the following numbers as a business or scientific man would:

2. 4573

3.

4.

7. 4506.34 12. 134.0561 17. 15.0045 3046 8. 2745.62 13. 305.2407 18. 25.4505 1908 9. 3709.36 14. 145.0045 19. 105.3462 5. 2647 10. 4325.05 15. 625.1073

20. 45.3207

22.

bers.

23.

11. 5405.26 16. 106.6372 21.

1.0562

Read the numbers in Exs. 2 to 6 as telephone num

How are house numbers read? Read the numbers in Exs. 2 to 6 in this manner.

6574

7. Addition.-Learn the addition combinations so thoroughly that 6 + 5 and 5+ 6 suggest 11 as quickly as d-o-g suggests dog. In adding 9 increase ten's digit by 1 and decrease unit's digit by 1. (5 1) = 54. In adding 8 decrease unit's digit by 2. = 73.

(5 — 2)

=

Thus, 45 +9 (40+ 10) + increase ten's digit by 1 and Thus, 65 + 8 = (60+10) +

EXERCISES

1. Give the sum of each digit and the one to the right; to the left. Give the sum of each digit and the one just

above it; just below it.

6 7

8

6

4 7

4 8

5

4

6

8

5 9 4

6

5

7

789 +∞ + ∞ ∞ 10

4

8

9 8 7

4

6

7 8

8

5 7 4 9 6

7

8

4

Give the following sums as quickly as possible:

87

5. Find the sum of each of the columns in 1.