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ADVANCED ARITHMETIC

PART I

INTERMEDIATE ARITHMETIC

NOTATION AND NUMERATION

1. How many places are required to write ten in figures? One hundred? One thousand ? Ten thousand ? One hundred thousand? One million? Ten million? One hundred million ?

2. Why is our system of writing numbers called a decimal system?

3. Using the figures 2, 8, 3, 9, 6, write the largest number possible. Read it.

4. Using the same figures, write the smallest number possible. Read it.

5. Write a number occupying five places which has no tens and no hundreds. Read it.

6. Using the figures 3 and 3, and as many O's as necessary, write :

(1) A number in which the left-hand 3 has ten times the value of the right-hand 3.

(2) A number in which the left-hand 3 has one hundred times the value of the right-hand 3.

(3) A number in which the left-hand 3 has one thousand times the value of the right-hand 3.

1

7. Compare the values of the 7's in 77; in 707; in 770; in 7007; in 7070; in 70,007.

The value of a figure in a number depends upon two things:

(1) Its value in the scale 1, 2, 3, 4, 5, 6, 7, 8, 9. (2) Its place in the number.

The figures 1, 2, 3, 4, 5, 6, 7, 8, 9, are called significant figures.

8. Keeping in mind the values of the significant figures, tell how many times the value of the right-hand figure is represented by the left-hand figure in 42; in 930; in 603; in 5010; in 8002.

9. Write a number which has the figure 2 in the units' place, and a figure in the tens' place which in that place expresses forty times as much.

Write in figures :
1. Seven hundred eight.
2. Nineteen thousand forty-two.
3. Sixty thousand five hundred nine.

4. Two hundred forty-six thousand three hundred sixty.

5. Eight hundred ten thousand six hundred forty-nine.

6. Three million one hundred eighty-four thousand two hundred four.

7. Ninety-one million fifty-seven thousand five hundred.

8. Five hundred six million.

9. Four hundred eighteen million twenty-eight thousand seven hundred thirty-two.

10. Six hundred million three hundred thousand one hundred.

Separate into groups, read aloud, and then write in words:

[blocks in formation]

By combining these letters according to these rules, any number may be written:

I. When a letter is followed by the same letter or by one of less value, add the values of the letters.

Thus, II = 2; XX = 20; XV = 15; LX = 60.

II. When a letter is followed by one of greater value, subtract the letter of less value from the letter of greater value. Thus, IV = 4; IX = 9; XL = 40;

XL = 40; CD= 400. 1. Write 1776 in Roman notation. 1776 = 1000 + 700 + 70 + 6

M + DCC + LXX + VI = MDCCLXXVI

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