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TAE Marine Review 75 = Vi -4 = 2-5; 625 == 94; 0375 = te-1G: sg 39-1000; .0064 = 4-625; .00625 = 1-160. To convert, or change common fractions to decimal fractions: Rule.--Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places in the quotient as there are ciphers annexed. Now, if you are not familiar with decimal fractions the first thing that will bother you is how is one to know that is .25; % is .5; % is .125, etc. Here is the way that it is done: add one or more ciphers to the numerator and divide by the denominator, thus % = 4 ). 1.00 25 2 ) 16 1-8 = 8 ) 1.000 5 5125 2-3 = 3 ) 2.000 .666 + or, .666 2-3. The sign + is sometimes placed after the result to indicate that there is still a remainder. Change 3% to a decimal fraction, equals 1375; 54 = 625; V4 = 75; 2-5: == A; 4-8 == 8) 1-3 == 33 4 Or 33 1-9; 49-50 = .7678 +; 10134 = 101.75; 114% = 11.125; 25% = 25.5; 40 1-3 = 40.33 I-3. Note.--In many cases the division is not exact. In such instances the remainder may be expressed as a common fraction, or the sign + may be employed after the decimal to show that the result is not complete; thus, 1-6 = .166 2-3 er .166 +. Addition of Decimals. Addition of decimals is performed exactly like that of whole numbers, placing the numbers of the same denom- ination under each other, in which case the decimal points will range straight in one column, thus: Examples-- Miles. Feet. Inches. 26.7 1.26 272.3207, 32.15 2.31 .0134 143.206 1.785 2.1576 '003 2.0 31.4 "202.059 7.355 305.8977 Rule--Write numbers so that decimal points stand in a column.. Add as in whole numbers, and place the point in the sum directly under the points above. Add the following, reducing common fractions to deci- Mais: 1834. +. 9.048 + 25 1-20 7 163 4+ 200 = 0075 = 218.715 Ans. What is the sum of 37 thousandths, 54 ten thousandths, 407 hundred thousandths and 12,345 millionths? So e7 thousandths 0054 ten thousandths .00407. hundred thousandths .012345 millionths 058815 , millionths Find the sum of $2534, $81.09; $1614; $.8714; $1502; and $7% = $275,215 Ans. : ae How many rods of fence will enclose a field the sides of which are respectively 34.72 rods; 48 11-25 rods; 152.17 rods; 953% rods, and 565% rods. Ans. 387.33 rods. Find the sum of 3-80, 2-7, 43-56, 7-24 and 75-436, in deci- mals, work to the fourth place. 1.55471. Do you thoroughly understand that when adding deci- mal fractions that you will have one decimal place when you add tenths and tenths, and two places when you add hundredths, and three for thousandths, four for ten-thous- andths, etc.? That you will also have two decimal places if you add tenths and hundredths, and three for tenths and thousandths, etc.? Now, we'll do a sum in common fractions, and then the same sum in decimal fractions. Atrw+wY=K- % expressed decimally is .25 = a % == es ew =, 875 Remember, that the addition of decimals is performed the same as in whole numbers, due regard, of course, being paid to the decimal point. See that the decimal points come directly under one another, just the same as degrees under degrees, minutes under minutes, etc. _. Add .§ and .75. Ans. 1 and 25 hundredths. ~ Add .02 and .005. Ans. 25 thousandths. : Add .25 and .125, also 4% and %. Ans. .375 and RK. Can you see that by adding tenths and hundredths that you will have two decimal places? If it bothers you to read and write the decimal when spelt out, this will probably help you some: that part of the decimal that has ths on the end of it is always the denoininator, as. twenty- five hundredths, hundredths is the denominator. How many decimal figures in the sum of tenths and tenths? Ans. one decimal place. Of tenths and hun- dredths? Ans. two places. Of hundredths and thousandths? Ans. Three places. Of tenths and thousandths? Ans. three places. : In adding several decimals, each having a different num- ber of decimal places, how many places will there be in the sum? Answer: the decimal point of the sum or amount will .be controlled by the greatest number of places of the deci- mals added. Note.--The denominator of a fraction is 100, the numerator i: what will express the decimal? Ans. Point, cipher, seven, read seven- hundredths; written .07.. The denominator is 1000, the numerator 35? Ans. Point, cipher, three, five, read thirty-five thousandths; written .035 (35-1000). In writing decimals, vacant orders must be filled with ciphers. SUBTRACTION OF DECIMALS. Subtraction of decimals is performed in the same manner as in whole numbers, by observing to set the figures of the same denomination and the decimal points directly under each other, thus: From 31.207 30.75 1.254 1364.2 : Take 2.63 .026 310 25.163 Differ. 28.637 36.724 .938 1339.037 Rule--wWrite the numbers so that the decimal point of the subtrahend is directly under the decimal point of the minuend, subtract as in whole numbers and place the point in the re- mainder directly under the point above. Or, write the sub- trahend under the minuend, so that units of the same order stand in the same column. Subtract as in subtraction of whole numbers, and place the decimal point before the order of tenths in the remainder; or, place the point in the remainder directly under the decimal point above. From 46.57 subtract 9.46325. 46.57000 = 46.57 9.46325 = 9.46325 37.10675 37.10075 Explanation :--The numbers are written so that units stand under units, tenths under tenths, etc. The decimals may be made similar and then subtracted, care being taken to place the decimal point in the remainder directly under the decimal point in the number subtracted. The ciphers may be supposed to be annexed when we subtract, and consequently need not be written. . ,