product of the numbers that represent its length, breadth, and thickness. The number of cubic units (cu. in., cu. ft., cu. yd., etc.) in a solid is called its volume. 1. How many cubic inches in a brick 8 in. long, 4 in. wide, and 2 in. thick? 2. How many cubic feet in a wall 16 ft. long, 4 ft. high, and 2 ft. thick? 3. A hole is 3 ft. long, 2 ft. wide, and 6 ft. deep. How many cubic feet of earth have been removed? 4. A cistern is 6 ft. square and 9 ft. deep. How many cubic feet of water will it hold? How many cubic yards? 5. How many cubic feet in a cord? A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high is called a cord. 6. How many cords are there in a pile of wood 16 ft. long, 4 ft. wide, and 4 ft. high? 7. A cubic foot of water weighs 1000 oz. What is the weight of a cubic yard of water? 8. Find the dimensions of a box that will hold 24 cu. in. of water. 9. What are the width and depth of a cistern 6 ft. long that will hold 144 cu. ft. of water? 10. An ice box holds 20 cu. ft. of ice. It is 4 ft. long and 2 ft. deep. How wide is it? 356. What part of A is dark? Into how many parts is each strip divided in B? What part of each strip is the shaded square? What part of the large square? Then of one-tenth of B is one of B. When anything is divided into ten equal parts, what is each part called? When each of these ten parts is divided into ten parts, how many parts are there? When each of these hundred parts is divided into ten parts, how many parts are there? When anything is divided into tenths, hundredths, thousandths, etc., the parts are called decimal parts; that is, tenth-parts. 357. You have already learned that 10 hundredths make 1 tenth, and that 10 tenths make 1 one, just as 10 ones make 1 ten, 10 tens 1 hundred, and so on. You have also learned that tenths and hundredths may be written with the decimal point and without denominators. Fractions so written are called Decimals or Decimal Fractions. 358. Tenths must stand next to ones, because 10 of them make 1 one; hundredths next to tenths, because 10 of them make 1 tenth. Next to hundredths we must write thousandths, because 10 of them make 1 hundredth, etc. 359. In decimals, as in integers (whole numbers), the position of the figures indicates their value. Thus, in 3.15 we know that the 1 is one-tenth, because tenths are written only in the first place to the right of ones; and that the 5 is five hundredths, because it is in the second place. 360. One-tenth of a cent is called a mill; then how many mills make 1 cent? How many mills in 10 cents? In 100 cents, or $1? Then 1 mill is what part of a dollar? What part of a cent are 5 mills, or 5 thousandths of a dollar? In $.125, how many dimes, cents, and mills? Which figure is in tenths' place? In hundredths'? In thousandths'? How many mills make 1 cent, or 1 hundredth of a dollar? How many mills in 1 dime? In 2 cents? Then may $.125 be read as 125 mills, or as 125 thousandths of a dollar? 361. Examine this table. Ten of any order make one of the next higher order. With reference to ones, where Thousandths. Ten-thousandths are tens and tenths written? Hundreds and hundredths? In what place is the 8? What does it express? In the decimal .125, there are 1 tenth, 2 hundredths, and 5 thousandths, or 125 thousandths. When there are no tenths or hundredths, we write thousandths in the third place, and put ciphers in the first two places. Thus, 5 thousandths is written .005. What decimal place is occupied by tenths? By thousandths? By hundredths? What occupies the second decimal place? The fourth? The third? Extend the table, and tell what occupies the fifth place. The sixth place. 362. In reading integers we omit the name, which is ones, the name of the lowest integral order. Decimals are read just as integers are, except that the name of the lowest decimal order is given. In reading an integer and decimal, use the word and between the integral and decimal parts of the number, but nowhere else. 325.46 is read 325 and 46 hundredths. .08 is read 8 hundredths. 517.325 is read 517 and 325 thousandths. 82.073 is read Thousandths occupy the third place, hence we write the 7 and put ciphers in the first two places, thus: .007. tenths, hence we put a cipher in the first place, thus: .025. Write as decimal fractions: 5 tenths 5 and 37 hundredths 75 thousandths 40 thousandths 90 hundredths 6 thousandths 82 thousandths 46 and 7 thousandths 75 and 14 thousandths 8 and 125 thousandths 92 and 8 thousandths 72 and 72 thousandths |