2. Supply the missing number in each of the following examples.

b

.0025812.054

1454.0650.14

How to Change a Common Fraction to a Decimal

You have learned that any common fraction may be regarded as an indicated division. Thus, may be regarded as 2÷5, and may be regarded as 3÷7. Since this is true, any common fraction may be reduced to a decimal fraction by performing the indicated division.

Reduce to a decimal fraction.

In case there is a remainder after the division is carried as far as desired, the quotient may be expressed as a complex decimal. In this case, 0.27211. If desired, the quotient may be expressed approximately, that is, as a decimal correct to any given number of places. Thus, .273, correct to three places, or .27, correct to two places.

The table at the top of the next page shows the decimal values of the more usual common fractions. It may be used now and later referred to. By memorizing this table you will be able to save much time when making computations.

1. Reduce each of the following to a decimal fraction.

2. Reduce each of the following to a complex decimal of three decimal places.

How to Find an Approximate Quotient

An approximate quotient is one that is nearly exact. It is sometimes desirable to find an approximate quotient, when using decimal fractions. The example solved below, together with the explanation, will make clear the meaning of an approximate quotient and show how one may be found.

.1957

247)48.361

24 7
23 66

22 23

1 431

1 235

1960

1729

231

In this example the quotient has been carried to ten-thousandths. Since 7 ten-thousandths is more than of 1 thousandth, the approximate quotient, correct to the nearest thousandth, is .196.

If the next number after the last one required is less than 5, the last one required remains unchanged. If the next number after the last one required is 5 or more, the last required number is increased by 1.

The quotient correct to tenths is .2.

The quotient correct to thousandths is .196.

Exercise 22

Find the quotients in the following examples correct to the nearest thousandth:

Find the quotients in the following examples correct to the nearest

9. The total weight of the 11 men on a college football team is 1894.2 pounds. What is the average weight to the nearest tenth of a pound?

10. Mr. Williams sold 27 lots for $26,555. What was the average selling price of each lot to the nearest cent?

11. The 47 cars on a freight train are loaded with coal. The total weight of the coal is 1641.24 tons. What is the average weight of the coal in each car? Find the result to the nearest tenth of a ton.

12. The total age of the 35 pupils in a seventh-grade class is 428.75 years. What is the average age to the nearest tenth of a year?

13. A racing automobile traveled 25 miles in 22.5 minutes. At this rate, how far would the automobile travel in 30 minutes? Find the answer to the nearest tenth of a mile.

REVIEW: DECIMAL FRACTIONS

1. The number of inches of rainfall in a city for each of the first five months of the year was as follows: 4.3, 4.7, 3.6, 5.2, 6.1. What was the average rainfall for the five months?

2. A gallon of water weighs 8.3 pounds. What is the weight of the water in a tank that contains 146.25 gallons?

3. A field of 18.5 acres yielded 451.7 bushels of wheat. What was the average yield per acre?

4. A cubic foot of water weighs 62.5 pounds, and a cubic foot of gold weighs 19.3 times as much.. What would be the weight of a cubic foot of gold? Of a cubic inch of gold?

5. Find the cost of 348 pounds of pork at $9.25 per 100 pounds. 6. Find the cost of 4250 envelopes at $2.60 per 1000. 7. Find the cost of 7850 bricks at $11.40 per 1000.

8. Find the cost of 4850 calendars at $1.10 per 100.

9. Mrs. Johnson paid $3.50 for a turkey which weighed 12.5 pounds. What was the price per pound?

10. The bank deposits and withdrawals of a merchant during a week were as follows:

What was the difference between the deposits and the withdrawals for the week?

11. Arrange the following fractions in order of size, placing the largest first: .09

.07984 .1024 .03786

12. An automobile traveled a mile in 52 seconds.

.061.

What was

the rate per hour?

13. The area of the United States is 3,026,789 square miles. In 1920 the population was 105,710,620. What was the population per square mile at that time?

14. Mr. Adams paid $28.40 for an automobile tire. At the end of 6142 miles the tire was worthless. What was the cost per mile for this tire?

15. The area of Texas is 265,896 square miles. The area of Rhode Island is 1248 square miles. How many times is the area of Rhode Island contained in the area of Texas?

16. A basketball team played 9 games and won 7. Another team played 8 games and won 5. What fractional part of the games played did each win? Which team made the better record? (Express the fractions as decimals.)

17. A boy raised 62.5 bushels of corn on .75 acres. Find the yield per acre.

18. In 1920 the population of the United States, exclusive of Alaska, was 105,710,620. The rural population was 51,406,017. How many hundredths of the total population for that year was the rural population?

19. Mr. Adams took an automobile trip of 114.8 miles. During the first hour he traveled 24.3 miles, during the second, 23.9 miles, during the third hour, 26.8 miles. At what average speed per hour was it necessary to travel to complete the trip in 3 hours?

20. A lot with sides that measure 86.5 ft., 72.2 ft., 84.9 ft., and 69.3 ft. was fenced with wire at $.32 a yard. What was the cost of the fencing?

21. George received a letter from his cousin William in London in which William said that he had accepted a position at 5 pounds a month. When the English pound is worth $4.3665, what does William's salary amount to in United States money?

22. Show by examples the effect of moving the decimal point one, two, or three places to the right. Show the effect of moving the decimal point one, two, or three places to the left.