143. Addition of Decimals is the process of finding the sum of two or more decimal numbers. 1. Add 375.83; 49.627; 5842.1963; 813.9762. SOLUTION.-Write the numbers so that the four decimal points may be in a column, the units 5, 9, 2, 3 in the first column to the left, the tenths 8, 6, 1, 9 in the first column to the right, etc.; then, adding as in simple numbers, place the decimal point in the sum between 1 and 6 under the column of decimal points. OPERATION. 375.83 49.627 5842.1963 813.9762 7081.6295 Rule.-1. Write the numbers so that the decimal points and figures of the same order may stand in the same column. 2. Add as in simple numbers. 3. Place the decimal point in the sum under the column of decimal points. 2. Add 37.1065; 432.07; 4.20733; 11.706. 485.08983 3. Add 4 and 4 ten-thousandths; 28 and 35 thousandths; 8 and 7 hundredths; and 9404 hundred-thousandths. 40.19944 A FRACTIONS 4. Find the sum of 3 units and 25 hundredths; 6 units and 4 tenths; and 35 hundredths. 5. Add 21.611; 6888.32; 3.4167. プ 10. 6913.3477 7231.0967 6. Add 6.61; 636.1; 6516.14; 67.1234; and 5.1233. 7. Add 4 and 8 tenths; 43 and 31 hundredths; 74 and 19 thousandths; 11 and 204 thousandths. 133.333 8. Add 45 and 19 thousandths; 7 and 71 hundredthousandths; 93 and 4327 ten-thousandths; 6 and 401 ten-thousandths. 151.49251 9. Add 432 and 432 thousandths; 61 and 793 tenthousandths; 100 and 7794 hundred-thousandths; 6.009; 1000 and 1001 ten-thousandths. 1599.69834 10. Add 16 and 41 thousandths; 9 and 94 millionths; 33 and 27 hundredths; 8 and 969 thousandths; 32 and 719906 millionths. 100. 11. Add 204 and 9 ten-thousandths; 103 and 9 hundred-millionths; 42 and 9099 millionths; 430 and 99 hundredths; 220.0000009. 999.99999999 12. Add 35 ten-thousandths; .00035; 35 millionths, and 35 ten-millionths. .0038885 SUBTRACTION OF DECIMALS. 144. Subtraction of Decimals is the process of finding the difference between two decimal numbers. 1. From 729.835 subtract 461.5738. SOLUTION.-Write the numbers so that the two decimal points may be in a column, the units 9 and 1 in the first column to the left, the tenths 8 and 5 in the first column to the right, etc.; then, subtracting as in simple numbers, place the decimal point in the remainder between 8 and 2 under the column of decimal points. OPERATION. 729.835 461.5738 268.2612 131. The orders of integers decrease from left to right in a tenfold ratio. Thus, in the number 1111, 1 thousand is 10 times 1 hundred, 1 hundred is 10 times 1 ten, and 1 ten is 10 times 1 unit. ORDERS OF DECIMALS. 132. 1. The orders may be continued from the order units toward the right by the same law of decrease. 2. Let the order units be separated from the order that follows by a point (.). 3. Then, in the number 1.111, 1st. Since the 1 to the left of the point is 1 unit, the 1 to the right of the point is 1 tenth; for 1 unit is 10 times. 2d. Since the first order from the unit is 1 tenth, the second order from the unit is 1 hundredth; for is 10 times TOO. 3d. Since the second order from the unit is 1 hundredth, the third order from the unit is 1 thousandth; for is 10 times Too 4th. In like manner it may be shown that 1 in the fourth order to the right from the unit is 1 ten-thousandth; 1 in the fifth order to the right is 1 hundred-thousandth; 1 in the sixth order is 1 millionth, etc. REM.-A number consisting of figures other than 1, might be used as well for the purpose of illustration. 4. The position of the integral and decimal places relative to the unit is exhibited in the following 5. The first order on the left of the unit is tens, the first order on the right of the unit is tenths; the second order on the left is hundreds; the second order on the right is hundredths, etc. DEFINITIONS. 133. 1. A decimal fraction, or decimal, is one or more tenths, hundredths, thousandths, etc., written like the orders of integers. 2. A decimal point is placed before the order tenths to distinguish the fraction. 3. The decimal orders increase from right to left, and decrease from left to right the same as the orders of integers. 4. The names of the orders of decimals are similar to the names of the corresponding orders of integers. 134. Conversion of the common fractions, 100, 1000, etc., to decimals. |