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18. Problems involving large numbers. In problems involving multiplications and divisions time and labor are saved by first indicating the multiplications and divisions and then performing them by cancellation.

EXAMPLE. The first Liberty Loan of the United States in the European War was $2,000,000,000. A silver dollar. is 1 in. in diameter. If 1,000,000,000 silver dollars were placed in a row just touching each other, they would make a row how many miles long? Neglect the fraction of a mile. SOLUTION. The indicated multiplications and divisions are

1,000,000,000×1.5
5280 X 12

Let the pupil complete the solution, canceling as far as possible.

Exercise 19

1. How many years and days will it take to count 1,000,000,000, counting at the rate of 150 a minute, and counting 8 hours a day?

2. In what year was an event that happened one billion minutes after the beginning of the Christian era?

3. If there are 3 birds to the acre in Illinois, and each bird destroys one-third of an ounce of insects a day, how many tons of insects are destroyed in 6 months of 30 days each? The area of Illinois is 56,650 square miles.

4. Light travels 186,000 miles per second. How long does it take light to travel from the sun to the earth, 93,000,000 miles?

5. Sound travels 1084 ft. per second. The distance from the earth to the moon is 240,000 miles. If you waved your handkerchief and at the same time said "Hello" to the "Man in the Moon," and if he received both signals, how long before he heard the hello would he see the handkerchief? Neglect the fractions of a second.

6. How many miles will light travel in a year of 3651 days?

7. The distance that light travels in one year is called a light year. The nearest fixed star is said to be 3.6 light years distant from the earth. How many miles distant is it?

8. It is thought that some stars are as far away as 100,000 light years. How many miles distant are they?

9. The distance from the sun to the planet Neptune is 2,792,000,000 miles. Neptune is how many times as far away from the sun as the earth?

10. The annual yield of wheat in the United States for ten years was as follows:

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11. The corn crop in the United States for a certain year was estimated to be three billion fifty-four million five hundred thirty-five thousand bushels, with a total value of one billion seven hundred fifty-five million eight hundred fiftynine thousand dollars. What was the estimated price a bushel?

19. Reduction of decimal fractions to common fractions. EXAMPLE 1. Reduce .625 to a common fraction in its lowest terms.

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EXAMPLE 2. Reduce .163 to a common fraction in its lowest terms.

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What are the steps in reducing decimal fractions to common fractions in their lowest terms?

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Rule. To reduce a decimal fraction to a common fraction, write the numerator over the denominator and reduce the result to its lowest terms.

20. Multiplication and division by powers of 10. The numbers 10, 100, 1000, and so on are called powers of 10. In multiplying and dividing by powers of 10 the pupils should use the following rules:

To multiply a number by a power of 10 move the decimal point as many places to the right as there are zeros in the multiplier. To divide a number by a power of 10 move the decimal point as many places to the left as there are zeros in the divisor. Since 25=100, we can multiply by 25 by multiplying by 100 and dividing by 4. Also we can divide by 25 by dividing by 100 and multiplying by 4.

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Exercise 21

1. Copy and fill out the following table. Multiply the numbers in the left-hand column by the number at the top of each of the other columns, and write the results in the vacant spaces.

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2. Make a similar table and divide each of the numbers 423.7, 100.2, .01, 423, 20.09, by each of the numbers 10, 100, 1000, 1,000,000.

3. Since 331-100, make rules for multiplying and for dividing by 331.

4. Since 125-1000, make rules for multiplying and for dividing by 125.

5. What part of 100 is 50? Make rules for multiplying and for dividing by 50; by 163;

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by 12; by 81.

13. 42.08X50=?
14. 8×240 ?

=

15. 842.96 16% = ?
16. 25×128.464 = ?
17. 125X.0424= ?
18. 1000÷331=?
19. 84X3325=?

MULTIPLICATION OF DECIMAL FRACTIONS 43

21. Multiplication of decimal fractions. Principle. The number of decimal places in the product of several decimals equals the sum of the numbers of decimal places in the factors.

EXAMPLE. Multiply 24.74 by .08.

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17. Gold is 19.3 times as heavy as water. A cubic foot of water weighs 62.5 lb. What is the weight of a cubic foot of gold?

18. Find the weight of a cubic foot of alcohol which is .79 as heavy as water.

19. A certain kind of steel bar weighs 3.83 lb. for each foot of length. Find the weight of such a bar 16 ft. long.

20. What is the cost of 450 bu. of wheat at $1.87 a bushel? 21. A certain type of steel bolt weighs .052 lb. each. Find the weight of 100 of these bolts; of 2000 bolts.

22. Another type of bolt weighs .143 lb. each. Find the weight of 500 of these bolts.

23. What is the cost of 31 yards of cloth at $1.30 a yard?

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