Art. 122. When fractions denoting tenths, hundredths, thousandths, etc., are expressed on a scale of ten, they are said to be expressed decimally. The right-hand figure is written in the order indicated by the name of the decimal. 20. Express decimally 25 hundredths. 28. Eight units and seven tenths. 29. Fifteen units and thirty-six hundredths. Art. 123. The fourth decimal order is called tenthousandths; the fifth, hundred-thousandths; and the sixth, millionths. 34. Express decimally 3205 ten-thousandths. 35. Express decimally 6008 hundred-thousandths. 36. Express decimally 40532 millionths. 37. Two hundred and seventeen ten-thousandths. 38. Four hundred and twenty-two millionths. 39. Seven hundred and twelve ten-thousandths. 40. Fifteen millionths. 41. Four hundred and one hundred-thousandths. Art. 124. An integer and a decimal, written together as one number, are connected by and when expressed in words. Thus, 45.14 is read forty-five units and fourteen hundredths. 42. Read 27.305. 43. Read 463.3028. 44. Read 7.06005. 45. Read 4000.004. 46. Express decimally forty-five units and fiftytwo hundredths. 47. Forty units and forty-five thousandths. 48. Two hundred units and seventy-nine millionths. DEFINITIONS, PRINCIPLES, AND RULES. Art. 125. A Decimal Fraction is a fraction whose denominator is some power of ten. The powers of ten are 10, 100, 1000, 10000, etc. Art. 126. Decimal fractions may be expressed in three ways: 1. By words; as, three tenths, twelve hundredths. 2. By writing the denominator under the numerator; as, 18%. 3. By omitting the denominator and writing the numerator decimally; as, .3 and .12. The denomi nator is understood. Three tenths,, and .3 each express the same decimal fraction, but the term decimal fraction is usually applied to written decimal fractions when they are expressed by the third method. Art. 127. The Decimal Point is a period placed at the left of the order of tenths, to designate the decimal orders. Art. 128. A Mixed Decimal Number is an integer and a decimal written together as one number; as 2.45. It is also called a Mixed Number. The orders on the left of the decimal point are integral, and those on the right are decimal. The decimal orders are called Decimal Places. Art. 129. The following table gives the names of six integral and six decimal orders: Integral Orders. Decimal Orders. Art. 130. PRINCIPLES.-1. The denominator of a decimal fraction is 1 with as many ciphers annexed as there are decimal places in the fraction. 2. The value of the successive decimal orders decreases tenfold from left to right, and increases tenfold from right to left. 3. The name of a decimal is the same as the name of its right-hand order. Art. 131. RULES.-1. To read a decimal, Read it as though it were an integer, and add the name of the right-hand order. NOTES.-1. A decimal is read precisely as it would be were the denominator expressed. 2. In reading a mixed decimal number, the word "units" may be omitted when this does not change the mixed number to a pure decimal. 2. To write a decimal, Write it as an integer, and so place the decimal point that the right-hand figure shall stand in the order denoted by the name of the decimal. NOTE. When the number does not fill all the decimal places, supply the deficiency by prefixing decimal ciphers. WRITTEN EXERCISES. 49. Write in words 4045.03007. 50. Write in words .040085. 51. Write in words 405.40071. 52. Write in words 35000.0094. 53. Express decimally five thousand and sixtysix millionths. 54. Eight hundred and forty-two ten-thousandths. 55. Seventy-five and four hundred and three hundred-thousandths. LESSON II. Reduction of Decimals. CASE I-DECIMALS REDUCED TO HIGHER OR LOWER ORDERS. 1. How many hundredths in 1 tenth? In 3 tenths? In 5 tenths? In .8? 2. How many thousandths in 1 hundredth? In 5 hundredths? In .12? In .25? 3. How many tenths in 10 hundredths? In 40 hundredths? In .50? In .60? In .80 ? 4. How many hundredths in 10 thousandths? In 30 thousandths? In .060? In .120? In .340? WRITTEN EXERCISES. 5. Reduce .325 to hundred-thousandths. Since the multiplication of both terms PROCESS. of a fraction by the same number does not .325.32500 325 = 1000 change its value (Art. 66) .325 or $5 32388.32500. 6. Reduce .45 to ten-thousandths. 7. Reduce 6.5 to thousandths. 8. Reduce 23 to hundredths. 9. Reduce 62.5 to ten-thousandths. 10. Reduce .048 to hundred-thousandths. 11. Reduce 406.062 to millionths. 12. Reduce .4500 to hundredths. PROCESS: .4500= .45, Ans. 13. Reduce .5000 to tenths. |