QUESTIONS 1. What will 8 yards of sheeting cost at 121 a yard? 2. What will 9 pounds of prunes cost at 9 a pound? 3. What is the cost of 7 lb. of butter at 22¢ per lb.? 4. What is the cost of 12 pounds of tea at 60₫ a pound? 5. What is the cost of 12 lb. of coffee at 30 per lb.? 6. What is the cost of 11 yards of cloth at $4 a yard? 7. What is the cost of 9 books at 40 each? 8. At $12 a cord, what will 12 cords of wood cost? 10 cords? 9 cords? 7 cords? 6 cords? 6 cords? 5 cords? 9. How many feet are there in 11 yards? 10 yards? 29 yards? 48 yards? 97 yards? 10. How many quarts are there in 10 gallons? 9 gallons? 8 gallons? 50 gallons? 11. If you buy 5 marbles for 1, how many marbles. can you buy for 11? 8? $1.00? 12. At 8 a quart, what will 12 quarts of milk cost? 11 quarts? 6 quarts? 24 quarts? 98 quarts? 17 quarts? 13. What will be the cost of 12 yards of braid at 10¢ a yard? 10 yards? 60 yards? 8 yards? 25 yards? 14. What is the cost of 8 yards of silk at $5 a yard? 15. If 7 yards of cloth make a suit, how many yards. will it take to make 8 suits? 16. How much do 9 pounds of ginger cost at 30¢ a pound? 17. At $12 apiece, what will 10 sofas cost? 18. What is the cost of 10 bbl. of vinegar at $9 per bbl.? 19. What will 11 pair of shoes cost at $5 a pair? 20. If 8 men can build a wall in 9 days, how long will it take 1 man to build it? NOTATION Notation is a method of writing numbers. The system of notation in general use is called the Arabic Notation. It was introduced into Europe in the twelfth century by the Arabs who founded the empire of the Moors in Spain. It came to Arabia from India. This notation uses ten characters of figures to express numbers. It is also called a decimal notation, because the numbers increase and decrease in a tenfold ratio. Figures, 1 2 3 4 5 6 7 8 9 0 Names, one two three four five six seven eight nine cipher The last figure, or character, is also called zero, or naught. It has no value when standing alone. The first nine figures are termed significant figures, as each always signifies a value of its own. These figures are also called digits. We express ten units by using not one figure, but two figures, 10. The cipher occupying the first place, at the right hand, gives a tenfold value to the 1, and shows that there are no units of the first order, or place. The 1 ten is a unit of the second order. The number 100, equal to 10 tens, is a unit of the third order, and, therefore, the digit 1 occupies the third place. In a decimal system of notation ten units of any order make one unit of the next higher order. 1 unit of the first order is expressed by 1 unit of the second order is expressed by 1 unit of the third order is expressed by 1 unit of the fourth order is expressed by 1 unit of the fifth order is expressed by 1 unit of the sixth order is expressed by 1. 10. 100. 1000. 10000. . 100000. Units of higher orders are written in the same way. NUMERATION Numeration is a method of reading numbers. In order that numbers may be read conveniently, they are grouped into periods of three orders each. Learn the names of the periods in the following table: 3 6 3, Hundreds of Quintillions. - Hundreds of Quadrillions. Tens of Quadrillions. Hundreds of Trillions. Tens of Trillions. Trillions. ∞ Hundreds of Billions. ∞ Tens of Billions. 1 54, 79 2, 8 8 3, 2 5 1, 3 6 6, 72 4. The periods in their order above Quintillions are Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quattuordecillions, etc., to Vigintillions. Numbers higher than these are seldom needed, except by astronomers in measuring the distances of the stars. If a number consists of more than one period, the lefthand period may contain one, two, or three figures, but all the other periods must have three figures in each period. Vacant orders are filled by ciphers. The system of numeration in use in England has six orders in every period. Hence in the English system a million is a thousand thousand, a billion is a million times a million, a trillion is a million times a billion, and so on. Point off the number into periods of three figures each, beginning at the right hand, and read each period as if it stood alone, naming its order. Do not use the word and in reading whole numbers. Ciphers are read only as they show the values of higher figures. 2. The world has 1,500,000,000 people, and $1,000,000000,000 worth of wealth. Write this statement in words. 3. Write in figures the following numbers: Twenty-eight thousand, three hundred nineteen. Three million, one hundred forty-five thousand, six hundred eighty-five. Eighty-six million, four hundred three thousand seven. Nine hundred nine million, ninety-nine thousand nine. One hundred forty million, six hundred two thousand seven. Seven hundred million, twenty thousand. Five billion, five million, five thousand five. Sixty trillion, sixty million seventy. Seventeen trillion, seven million seventy. Eight billion, seventy million, four hundred thousand, two hundred seventy-six. DECIMAL FRACTIONS The powers of a number are its products when multiplied one or more times by itself. The first power is the number itself. 2 x 24. 4 is the second power of two The powers of 10 are 10, 100, 1000, 10,000, etc. are called the first, second, third, fourth of ten. 10 x 10 x 10 = These powers 1000. 1000 is the third power of 10. A fraction which has for its denominator one of the powers of 10 is called a decimal fraction, or a decimal. All other fractions are called common fractions. To simplify the writing of the denominators of decimal fractions, a method of notation is used by which we express the value of the denominator in every case by the decimal form of writing the numerator. .3 stands for 3, and is read three tenths. .25 stands for 25, and is read twenty-five hundredths. .347 stands for 3476, and is read three hundred fortyseven thousandths. 1000' In each case the figures that follow the decimal point form the numerator of the fraction. The number of figures that follow the point corresponds to the number denoting the particular power of 10 that forms the denominator of the fraction. As the first power of 10 is 1 followed by zero, and the second power of 10 is 1 followed by two zeros, and the third power of 10 is 1 followed by three zeros, etc., in every case we can write the denominator by affixing to 1 a number of zeros equal to the number of figures that follow the decimal point. |