NOTATION AND NUMERATION Millions 1. How many thousands make 1 ten-thousand? 2. How many ten-thousands make 1 hundred-thousand? Similarly, 10 hundred-thousands are grouped to make 1 million; 10 million are grouped into 1 ten-million, and 10 ten-millions are grouped into 1 hundred-million. The three places, millions', ten-millions', and hundred-millions', belong to millions' period. The following table shows the names of the first nine places or orders and the first three periods for integers. The number used for illustration is six hundred seventy-five million, three hundred twenty-one thousand, five hundred thirty-six. The period at the left in a number may not be complete. That is, it may contain only one or two figures, as in 6,000 or in 65,000,233. How many must the other periods contain? Each period beginning at the left is read as if it were a number by itself, the name of the period being added except in the case of units' period when it is understood. 5 HUNDREDS co TENS 3 UNITS (Ones) 118 PROBLEMS-NOTATION AND NUMERATION 1. A merchant gained $1,325.75 the first year, $2,195.50 the second year, and lost $989.85 the third year; how many dollars did he gain in the three years? 2. A ranchman paid $565 for sheep, $1,250 for cattle, and $863 for horses; how much had he left out of $3,000? 3. A landowner received $25,673 from the sale of lands, $2,565 for rent, and expended $565 for repairs; how much had he left? 4. A man started in business with $2,765.25 in cash and a stock of goods worth $5,850.25. At the end of the first year he has $3,650.50 in cash and a stock of goods worth $4,985. Has he gained or lost, and how much? 5. A man bought a horse and carriage for $300.50. He sold the horse for $125 at a loss of $50.50. What was the cost of the carriage? 6. The coinage of gold at the United States mints in 1880 was $62,308,279, in 1900 it was $99,272,942.50; how much more was coined in 1900 than in 1880? 7. Find the total coinage for each year from the following table: 8. Read each result in Exercise 7. How many periods are there in each result? Name them. Write in numerals: 9. Eight million. 10. Eighty-five million. II. Four million two hundred seventy-five thousand. PROBLEMS-STATISTICS 119 1. Read the numbers in the statement of the New York banks for the last week of December, 1903: The week's averages of the New York banks compare as follows with the same date one and two Bring similar items cut or copied from newspapers or magazines and read the numbers in class. 2. Read: The numbers of people speaking various languages in 1801 and in 1890 were: 3. From Exercise 2 find the total number of people speaking the seven languages in 1801; in 1890. 4. Find how many more people spoke each language in 1890 than in 1801. 5. Which language was spoken by the most people in 1801? How many more people used it than used each of the other languages? 6. Answer the questions of Exercise 5 for the year 1890. 52,250 1,828,697 Nevada..... 110,700 590,884 63,592 New H'pshire 113,020 122,931 New Jersey.. 42,335 9,305 411,588 7,815 1,883,669 Arkansas.. 53,850 1,311,564 New Mexico. 122,580 195,310 California.. 158,360 1,485,053 New York... 49,170 7,268,894 Colorado..... 103,925 539,700 N. Carolina.. 52,250 1,893,810 Connecticut.. Delaware.. Dist. of Col... Florida .. Georgia.... Hawaii... Idaho... Illinois.. Indiana. Indian Ty. Iowa... Kansas Kentucky... Louisiana. Maine... Maryland... 4,990 908,420 N. Dakota.. 2,050 184,735 Ohio... 70,795 319,146 41,060 4,157,545 39,030 398,331 70 278,718 Oklahoma Ty 58,680 528,542 Oregon...... 96,030 413,536 59,475 2,216,331 Pennsylvania 45,215 6,302,115 6,449 154,001 Rhode Island 84,800 161,772 S. Carolina.. 56,650 4,821,550 S. Dakota... 1,250 428,556 30,570 1,340,316 77,650 401,570 36,350 2,516,462 Tennessee... 42,050 2,020,616 31,400 392,060 Texas.. 265,780 3,048,710 84,970 276,749 9,565 343,641 42,450 1,854,184 48,720 1,381,625 Washington.. 69,180 518,103 33,040 694,466 W. Virginia.. 24,780 958,800 12,210 1,188,044 Wisconsin... 56,040 2,069,042 Massachusetts 8,315 2,805,346 Wyoming.... 97,890 Michigan.... 58,915 2,420,982 69,415 3,106,665 Philippine Is. 140,000 8,000,000 146,080 243,329 Porto Rico.. 3,600 953,243 77,510 1,066,300 Samoan Isl'ds 79 5,800 1. The total population, excluding that of possessions, is 76,303,387; what is the total including them? Find the total area and population of the states bordering on: 2. The Atlantic Ocean. 3. The Pacific Ocean. RATIO AND AVERAGE Ratio Oral. 1. What part of 9 qt. are 2 qt.? are 5 qt.? 3 qt.? 7 qt.? 2. What part of 10 bu. are 2 bu.? are 4 bu.? 5 bu.? 8 bu.? 3. What fraction of 7 days are 2 days? are 3 days? 5 days? 6 days? 4. What fraction of 1 square foot is 1 sq. in.? 12 sq. in.? 36 sq. in.? 72 sq. in.? 5. What fraction of a day is 1 hr.? 1 hr. 45 min.? 6 hr.? 6 hr. 15 min.? 6. What part of 1 is? What part of is? 7. What fraction of $1 is 1634? 25¢? 331¢? 371⁄2¢? 6714? 8. What part of 12 is 4? What is the quotient of 4 divided by 12? The quotient of two numbers is often called their ratio. The questions What part of 12 is 4? 4 ÷ 12? What is the ratio of 4 to 12? are all answered by the fraction. 9. State the ratio of 16 oz. to 20 oz.; of 10 min. to |