10. EXERCISE. Read in two ways as suggested in the following: 324.61. (1) 3 hundreds, 2 tens, 4 primary units, 6 tenths, 1 hundredth. (2) Three hundred twenty-four and sixty-one hundredths. Use the word and in place of the decimal point only. Observe that any number may be read by giving the name of the units denoted by the right-hand figure to the entire number; thus, 146 is 146 primary units; 21.8 is 218 tenths; 3.25 is 325 hundredths. 1. 272 tens + 7 primary units = 27 primary units. 2. 2.7 2 primary units + 7 tenths = 3. .27 4. .027 sandths. = == 2 tenths+7 hundredths tenths. hundredths. 5. .436 = = 4 tenths 3 hundredths + 6 thousandths thousandths. = 6. 5.2475 primary units + 2 tenths + hundredths + 7 thousandths = 7. 3.24 = 8. 5.206 9. 25.13 10. 14.157 11. 275.4 NOTE. = = 5247 -ths. hundredths. thousandths. hundredths. thousandths. Exercise 11 and Exercise 12 are important as a prepar ation for the clear understanding of division of decimals. 12. EXERCISE. Observe that any part of a number may be read by giving the name of the units denoted by the last figure of the part to the entire part; thus, 24.65 is 246 tenths and 5 hundredths; 14.275 is 1427 hundredths and 5 thousandths. In a similar manner read each of Observe that in reading a mixed decimal in the usual way, we divide it into two parts and give the name of the units denoted by the last figure of each part to each part; thus, 2346.158 is read 2346 (primary units) and 158 thousandths. Read the following in the usual manner. Do not use the word and in reading the numbers in the second column: 1. Two hundred and eight thousandths. 4. Six hundred twelve thousandths. 16. Note the number of decimal places in each of the following expressions: 1. 4 4 tenths. (1 decimal place.) = 2. .2727 hundredths. (2 decimal places.) 3. .346 346 thousandths. (3 decimal places.) = 4. .27582758 ten-thousandths. 5. .07286 = 7286 hundred thousandths. 6. .000896 896 millionths. (6 decimal places.) billionths. (9 decimal places.) 7. .000,468,275 = 8. .000,000,000,462 = = trillionths. 9. .000,000,000,000,527 quadrillionths. 10. In any number of thousandths there are decimal places. 11. In any number of millionths there are places. decimal 12. In any number of billionths there are decimal places. 13. In any number of hundredths there are places. decimal 14. In any number of ten-thousandths there are decimal places. 15. In any number of hundred thousandths there are decimal places. Algebra-Notation. 17. Letters are used to represent numbers; thus, the letter a, b, or c may represent a number to which any value may be given. 18. Known numbers, or those that may be known without solving a problem, when not expressed by figures, are usually represented by the first letters of the alphabet; as, a, b, c, d. ILLUSTRATIONS.. (a) To find the perimeter of a square when its side is given. Hence the rule: Let a one side.* Then 4 a = the perimeter. To find the perimeter of a square, multiply the number denoting the length of its side by 4. Hence the rule: To find the perimeter of an oblong, multiply the sum of the numbers denoting its length and breadth by 2. 19. Unknown numbers, or those which are to be found by the solution of a problem, are usually represented by the last letters of the alphabet; as x, y, z. (a) There are two three times the first. Let Then ILLUSTRATION. numbers whose sum is 48, and the second is What are the numbers? * That is, the number of units in one side. The letter stands for the number. 20. The sign of multiplication is usually omitted between two letters representing numbers, and between figures and letters; thus, a x b, is usually written ab; b x 4, is written 4 b. 6 ab, means, 6 times a times b, or 6 × a × b. 21. EXERCISE. Find the numerical value of each of the following expressions, if = 8, b = 5, and c = 2: απ Find the numerical value of each of the following expressions if a = 20, b = 5, and c = 2: 2. 2(a - b) = 3. 4(a+b+c) = 7. (a+b)+3c= |