35. By how much does 175 hundredths exceed 175 hundred-thousandths? What is the ratio of the first number to the second?

36. By how much does $1 exceed 1 mill? 37. By how much does $2 exceed 15 mills?

323 hundredths x 25 8075 hundredths 80.75.

Example 2. Multiply 3.23 by .25.

Since the multiplier is

=

of 25, the product 3.23 ×

.25 of 3.23 × 25. 1 of 80.75= .8075.

=

The mechanical work of multiplying may be performed as follows:

3.23

.25

1615

646

.8075

Multiply as if both numbers were integers, and point off in the product, commencing at the right, as many places as there are decimal places in both multiplicand and multiplier.

To square a number means to multiply the number by

itself or to take the number twice as a factor.

To cube a number means to take the number three times as a factor.

EXERCISE 35

1. Find .04 of $108; .05 of $274; .06 of $720; .07 of $144.

2. Find .09 of $34.50; .3 of $75.30; .08 of $75.80; .07 of $84.70.

3. Find .4 of $29.75; .5 of $69.48; .6 of $68.32; .1 of $328.50.

4. Find .125 of $80.80; .75 of $54; .6 of $300.50; .25 of $98.84.

5. Find .625 of $688; .875 of $792.80; .375 of $900.80.

6. Find .375 of 84 acres; .0625 of 64 acres; .3125 of 96 acres.

38. .7645 of the asphalt found in West Virginia is composed of carbon, .0783 is hydrogen, .1346 is oxygen, and the remainder is ash. How much of each constituent is

in 254 tons of asphalt?

Check your answers.

39. .7217 of the asphalt found in Oregon is composed of carbon, .079 of hydrogen, .1461 of oxygen, and the remainder of ash. Find the amount of each in 385 tons of asphalt. Check your answer.

40. Multiply the square of 14 by .7854.

41. The area of the surface of a sphere is obtained by multiplying the square of the diameter by 3.1416. Find the area of the surface of the earth, taking the diameter to be 7,920 miles. Compare your answer with the area given in your geography.

42. The moon is nearly 2,200 miles in diameter. Find the area of its surface in square miles.

43. The velocity of the earth in its orbit is 18.5 miles. per second. How far does it go in 1 minute? in 1

hour?

44. A hurricane moves at the rate of 146.6 feet per second. How far does it travel in 1 minute? in 1 hour? 45. One meter = 39.37 inches. Find in inches the difference between 64 meters and 70 yards.

DIVISION

Before undertaking Division, it may be well to lay stress on the fact that numbers in the decimal system of notation may be read in many ways. Thus, 32.25 may be read, (a) 32 and 25 hundredths; (b) 3,225 hundredths; (c) 32,250 thousandths; (d) 322,500 ten-thousandths; (e) 322.5 tenths; (f) 3.225 tens.

Example 1. Divide 1.293 by 8.

8)1.293000

.161625

8 into 12 tenths gives 1 tenth, with a remainder 4 tenths. 4 tenths 40 hundredths;

=

40 hundredths and 9 hundredths = 49 hundredths. 8 into 49 hundredths gives 6 hundredths, with a remainder 1 hundredth. Change 1 hundredth to thousandths, and proceed as before.

Example 2. Divide .01234 by 4.

The work calls for no explanation.

4).012340

Find the difference between .07858 and .078; also find the difference between .07858 and .079.

.07858 .07900 .078 .07858 .00058 .00042

Hence .07858 is nearer to .079 than it is to .078. If, therefore, one is asked to give the value of .07858 correct to three figures, write for answer .079.

Express .73948 correct to three figures. Ans. .739. Express .25764 correct to three figures. Ans. .258. Whenever asked to give a decimal correct to any number of figures, discard the remaining figures if the first

one of them is less than 5; if it is 5 or more than 5, increase the last figure by 1.

Example 1. Divide .0732 by .8.

Make the divisor an integer by moving the decimal point one place to the right. Make a corresponding change in the dividend. This change is equivalent to multiplying divisor and dividend by 10.

8).7320

.0915

Example 2. Divide 12 by .125.

Move the decimal point in the divisor and in the dividend three places to the right, i.e. multiply each by 1,000.

96

125)12000

1125

750

750

Example 3. Divide 3.274 by 6.25.

.523+

625)327.400

3125

1490

1250

2400

1875

525

Whenever the divisor is a decimal, make it an integer by moving the decimal point to the right. Make a corresponding change in the dividend. After doing this, proceed in exactly the same manner as in long division of integers. Write the decimal point in the quotient in the same vertical line with the decimal point in the dividend transformed.