Beginning with the 2 feet, we say 2 times 6' are 12'-1 square foot: then, 2 times 25 are 50, and 1 to carry are 51 square feet. Next, 7 times 6' are 42",=3′ and 6": then 7' times 25=175' 14 7': hence, the surface is 65 10' 6", and by multiplying by the thickness, we find the solid contents to be 214 1' 1" 6" cubic feet. 2. Multiply 9ft. 4in. by 8ft. 3in. 214 1' 1" 6" 6. How many cords and cord feet in a pile of wood 24 feet long, 4 feet wide, and 3 feet 6 inches high? 7. How many square feet are there in a board 17 feet 6 inches in length, and 1 foot 7 inches in width? 8. What number of cubic feet are there in a granite pillar 3 feet 9 inches in width, 2 feet 3 inches in thickness, and 12 feet 6 inches in length? 9. There is a certain pile of wood, measuring 24 feet in length, 16 feet 9 inches high, and 12 feet 6 inches in width. How many cords are there in the pile? 10. How many square yards in the walls of a room, 14 feet 8 inches long, 11 feet 6 inches wide, and 7 feet 11 inches high? 11. If a load of wood be 8 feet long, 3 feet 9 inches wide, and 6 feet 6 inches high, how much does it contain? 12. How many cubic yards of earth were dug from a cellar which measured 42 feet 10 inches long, 12 feet 6 inches wide, and 8 feet deep? 13. What will it cost to plaster a room 20 feet 6' long, 15 feet wide, 9 feet 6′ high, at 18 cents per square yard? 14. How many feet of boards 1 inch thick can be cut from a plank 18ft. 9in. long, lft. 6in. wide, and 3in. thick, if there is no waste in sawing? DECIMAL FRACTIONS. 200. There are two kinds of Fractions: Common Frac tions and Decimal Fractions. A Common Fraction is one in which the unit is divided into any number of equal parts. A Decimal fraction is one in which the unit is divided according to the scale of tens. 201. If the unit 1 be divided into 10 equal parts, the parts are called tenths. If the unit 1 be divided into one hundred equal parts, the parts are called hundredths. If the unit 1 be divided into one thousand equal parts, the parts are called thousandths, and we have similar expressions for the parts, when the unit is further divided according to the scale of tens. These fractions may be written thus : From which we see, that in each case the denominator indicates the fractional unit; that is, determines whether it is one-tenth, one-hundredth, one-thousandth, &c. 202. The denominators of decimal fractions are seldom written. The fractions are usually expressed by means of a period, placed at the left of the numerator. Thus, is written .4 .45 .125 .1047 200. How many kinds of fractions are there? What are they? What is a common fraction? What is a decimal fraction? 201. When the unit 1 is divided into 10 equal parts, what is each part called? What is each part called when it is divided into 100 equal parts? When into 10000? Into 10,000, &c.? How are decimal fractions formed? What gives denomination to the fraction! This method of writing decimal fractions is a mere language, and is used to avoid writing the denominators. The denominator, however, of every decimal fraction is always understood: It is the unit 1 with as many ciphers annexed as there are places of figures in the decimal. The place next to the decimal point, is called the place of tenths, and its unit is 1 tenth. The next place, to the right, is the place of hundredths, and its unit is 1 hundreth; the next is the place of thousandths, and its unit is 1 thous andth; and similarly for places still to the right. NOTE. Decimal fractions are numerated from left to right; thus, tenths, hundredths, thousandths, &c. 202. Are the denominators of decimal fractions generally written? How are the fractions expressed? Is the denominator understood? What is it? What is the place next the decimal point called? What is its unit? What is the next place called? What is the third place called? What is its unit? numerated? What is its unit? Here we see, that the same figure expresses different decimal units, according to the place which it occupies: therefore, The value of the unit, in the different places, in passing from the left to the right, diminishes according to the scale of tens. Hence, ten of the units in any place, are equal to one unit in the place next to the left; that is, ten thousandths make one hundredth, ten hundredths make one-tenth, and ten-tenths, the unit 1. This scale of increase, from the right hand towards the left, is the same as that in whole numbers; therefore, Whole numbers and decimal fractions may be united by placing the decimal point between them: thus, A number composed partly of a whole number and partly of a decimal, is called a mixed number. RULE FOR WRITING DECIMALS. Write the decimal as if it were a whole number, prefixing as many ciphers as are necessary to make it of the required denomination. RULE FOR READING DECIMALS. Read the decimal as though it were a whole number, adding the denomination indicated by the lowest decimal unit. Write the following numbers in figures, and then numerate them. 1. Forty-one, and three-tenths. 2. Sixteen, and three millionths. 3. Five, and nine hundredths. 6. Two, and three hundred millionths. 7. Four hundred, and ninety-two thousandths. 8. Three thousand, and twenty-one ten thousandths. 9. Forty-seven, and twenty-one hundred thousandths. 10. Fifteen hundred, and three millionths. 11. Thirty-nine, and six hundred and forty thousandths. 12. Three thousand, eight hundred and forty millionths. 13. Six hundred and fifty thousandths. 203. Does the value of the unit of a figure depend upon the place which it occupies? How does the value change from the left towards the right? What do ten units of any one place make? How do the units of the place increase from the right towards the left? How may whole numbers be joined with decimals? What is such a number called? Give the rule for writing decimal fractions. Give the rule for reading decimal fractions, |