21, After selling of a barrel of oil, the grocer had 9 gallons left. How many gallons had he at first?

22. What is the sum of the ages of 5 children whose ages are, respectively, 65 years, 8 years, 10 years, 71⁄2

years, and 91 years? What is the average age?

23. A farmer can mow a piece of grain in 4 hours. His son can mow it in 6 hours. If both work together, what part of the piece can they mow in 1 hour?

24. A gardener planted 80 geraniums. 24 of them died. What part lived?

25.XA plumber is paid $4 a day, and his helper gas much. How much is paid to both?

DECIMALS

A power of a number is the product obtained by using that number as a factor a specified number of times. Thus, the second power of 10 is 10 x 10, or 100; the third power of 10 is 10 x 10 x 10, or 1000; and so on.

Fractions whose denominators are 10, 100, 1000, etc., as 10, 100, 1000, that is, common fractions whose denominators are 10, or some power of 10, are decimal fractions.

When the denominators are expressed by a decimal point, as in .7, .07, .007, such fractions are called decimals. The word "decimal" comes from the Latin word decem, which means ten.

When a decimal fraction is expressed as a decimal, there are as many places in the decimal as there are O's in the denominator of the decimal fraction. Thus, .9; 180.09; 1000 = .009; 10800.0009; and so on.

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When a decimal is expressed as a common fraction, the denominator is 1 with as many ciphers annexed as there are places in the decimal. Thus, .7; .07180; .007100000071000; and so on.

Write as common fractions: .9 .13 .217

Always treat a decimal as if it were a whole number.

The decimal point simply tells the kind of things with which we are dealing; that is, it gives a name to the decimal.

READING AND WRITING DECIMALS

The following table shows the method of reading and writing decimals.

Names and order of places must be memorized. A decimal takes its name from its denominator. 1. Read .0425.

Read the numerator as you would any whole number four hundred twenty-five. 425 what? The place of the last figure in the numerator shows the name of the denominator. The last figure, 5, stands in the fourth, or ten-thousandths' place. Therefore, we read four hundred twenty-five ten-thousandths

2. Read .000007.

Seven what? The figure 7 stands in the sixth or millionths' place. We read, seven millionths.

3. Read: .1; .01; .001; .0001; .00001; .000001.

The whole number is 27; the decimal is 56 hundredths. Using the word "and" to mark the decimal point, we read, twenty-seven and fifty-six hundredths.

In order to avoid confusion in reading numbers, use the word "and" only to mark the separation between a whole number and a decimal. Thus, 106.07 is read one hundred six and 7 hundredths.

Numbers consisting of a whole number and a decimal are mixed decimals.

58. How many decimal places are required to express tenths? To express hundredths? Thousandths? Tenthousandths? Hundred-thousandths? Millionths?

59. Write the figure 6 so that it shall express tenths; hundredths; thousandths; ten-thousandths; hundredthousandths; millionths.

60. Write in figures six hundred eight ten-thousandths. Ten-thousandths shows that the last figure of the decimal stands in the fourth decimal place, so we write .0608.

61. Write in figures six hundred and eight ten-thousandths. The whole number is 600, the decimal .0008: 80 we write 600.0008.

Write in figures:

62. Seven and three hundredths.

63. Nine thousandths.

64. Two hundred eighty-six ten-thousandths..

65. Two hundred and eighty-six ten-thousandths. 66. Seven hundred fifty-two hundred-thousandths. 67 Thirty-six and eight hundred-thousandths.

68. Five hundred twenty-seven millionths.

69. Nine and three thousand forty-six millionths.

70. Seventeen and one hundred three ten-thousandths

71. Sixty and sixteen ten-thousandths.

72. Four and four thousandths.

73. Four hundred and four thousandths.

74. Four hundred four thousandths.

CHANGING DECIMALS TO COMMON FRACTIONS

Oral

1. What is the denominator in .2? .7? .12? .08? .125? .015? .004?

2. Change .08 to a common fraction in its lowest terms.

To change a decimal to a common fraction, write the numerator over the denominator expressed in figures, and change to lowest terms.

Such expressions as .6, .375, .006, that is, decimals in which the numerator is a whole number, are simple or pure decimals.

Such expressions as .331, .371, .144, that is, decimals in whose numerator there is a common fraction, are complex decimals.

Name the common fractions equivalent to:

5. .1 .2 .3 .4 .5 .6 .7 .8 .9 6. .10 .20 .30 .40 .50 .60 .70 .80 .90