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 num ber 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 thou sand 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 hundred. fifty-seven thousand five 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: 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; CD = 400. 1. Write 1776 in Roman notation. 1776 = 1000 + 700 + 70 + 6 M + DCC + LXX + VI = MDCCLXXVI 22. Write MDCLXVI in Arabic notation. MDCLXVI = M + DC + LX + VI A dash over a letter increases its value one thousand tuld. Thus, X=10,000; L = 50,000. 38. Write these letters so that they shall represent 1000 times their ordinary value: I V C D M 39. Where are Roman numerals used? Numbers may be expressed in three ways: (1) by words; (2) by figures; (3) by letters. 40. In each of these three ways express your age; the number of days in a week; the number of months in a year; the number of weeks in a year; the number of minutes in an hour; the number of hours in a day; this page of the book; this year; the year in which you were born. Addition is the process of uniting two or more numbers into one number. What is the sign of addition? What is it called? What does it show? What name is given to the result in addition? Add 2 to each number in the diagram. Add 1; 3; 4; 5; 6; 7; 8; 9. Find the sum of the numbers in the diagram. Begin. ning with 1; 2; 3; 4; 5; 6; 7; 8; 9, add the numbers in the diagram. To each number in the table add 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12. To each number add 10; 20; 30; 40; 50; 60; 70; 87 +406; think 127, 133; say 133. Add other numbers to the numbers in the table. 80; 90. |