Review.

1. What is a Decimal Fraction? Give an example. Why are decimal fractions so called? In integers, how does the value of orders increase and decrease? In decimals, how does the value of the fractional units increase and decrease?

2. What is meant by Numeration of Decimals? In naming decimals, what is one tenth of one called? One tenth of one tenth? One tenth of one hundredth? One tenth of one thousandth? One tenth of one millionth? How many tenths make one? What make one tenth? One hundredth? One thousandth? One ten

thousandth? One hundred-thousandth? Repeat the rule.

3. What is meant by Notation of Decimals? In what two ways may decimals be expressed? When a decimal is expressed in decimal form by one figure, what does it denote? When expressed by two decimal figures, what does each denote? By three decimal figures? By five? By seven? How many decimal figures are needed to express tenths? Hundredths? Thousandths? Millionths? Ten-thousandths? Ten-millionths? Repeat the rule.

4. What is a Decimal Unit? Name the first order of decimal units; the fourth; the seventh; the second; the fifth; the eighth; the third; the sixth; the ninth. In what place are tenths? Ten-thousandths? Ten-millionths? Hundredths? Hundred-thousandths?

Hundred-millionths? Hundredths? Thousandths? Millionths? What two values has a decimal figure? Upon what does the local value of a decimal figure depend? State the general principles of decimals.

SECTION XV.

ADDITION OF DECIMALS.

1. How many ones in 5 ones and 7 ones? Tens and ones?

2. How many tenths in 3 tenths and 4 tenths?

and?

3. What is the sum of and? Of .7 and .8?

4. Find the sum of 5 hundredths and 10 hundredths.

Of and; of .05 and .75; .12 and .88.

5. Can 2 tens and 7 ones be directly added? 2 tenths and 7 hundredths? and? Why?

6. What is the sum of and 5? Of .5 and .07?

7. What is the sum of .05 and .09? How many hundredths and tenths? Of .07 and .08?

8. Find the sum of 8 and. .6? 5 and .07? .4 and .08? 3+.9 + .05?

Of 7 and 5? Of 6 and

6

9. Find the sum of 130, 150, and T.

Of .4, .06, .007.

10. What kind of fractions only can be added? When only can orders of decimal units be added?

332. Principle.

Only similar orders of decimal units can be added.

Written Exercises.

333. Example. - Find the sum of 7.8, 15.725, 8.08, and

.8765. SOLUTION.

7.8

15.725

8.08

.8765

32.4815

EXPLANATION. - Since only like orders of decimal units can be added, write the parts so that figures expressing units of the same order shall stand in the same column, and the decimal points in a column.

Begin at the lowest order at the right, and add as in integers, placing the decimal point before tenths in the sum, giving 32.4815, the sum required.

334. Rule for Addition of Decimals.

I. Write the numbers so that units of the same order shall stand in the same column.

II. Add as in addition of integers, and place the decimal point before the order of tenths in the sum.

Find the sum of

6. 82.765+ 8000 + .0075 + 87.1 + .00876 + 30.02. 7. $27.50 + $.125 + $300 + $98.625 + $17625.50. 8. 30 miles 8.025 miles + 1000 miles + 350.0025 miles. 9. Add together 8 tenths, 25 hundredths, 78 ten-thousandths, 5 millionths, and 2004 hundred-thousandths.

10. Find the sum of 24 hundreds, 24 tens, 24 ones, 24 tenths, 24 hundredths, and 24 thousandths.

11. A coal-dealer sold in four weeks 75.75 tons, 125.8 tons, 90.0625 tons, and 50.825 tons. How many tons in all?

12. A grocer bought a ton of coal for $6.75, a barrel of flour for $8.125, a chest of tea for $28.25, and a hogshead of molasses for $22.375. What did all cost?

SECTION XVI.

SUBTRACTION OF DECIMALS.

1. How many tenths are 7 tenths less 4 tenths?

?.7 and .2?

2. What is the difference between and 3. From 15 hundredths take 5 hundredths. From 25

take 180. From .75 take .05. From 1 take .25.

5

4. From take 100.

75 1000

5. What is less Too?

From .025 take .007.

100

6. What is the difference between .09 and .009? 2 and .02?

7. Find the value of 1% .4; .08 .008.

8. When only can one decimal fraction be taken from another?

335. Principle.

Only similar orders of decimal units can be taken one from another,

Written Exercises.

336. Example. - From 8.75 take .0875.

SOLUTION.

8.7500 8.75 .0875 Or, .0875

8.6625

8.6625

EXPLANATION. - Since only similar orders of decimal units can be taken one from another, write the numbers so that figures expressing units of the same order shall stand in the same column.

Annex two ciphers to the minuend to make the number of decimal places equal to the subtrahend; or regard them as annexed, and subtract as in integers, placing the decimal point before the order of tenths in the difference, giving 8.6625, the difference required.

337. Rule for Subtraction of Decimals.

I. Write the subtrahend under the minuend so that units of the same order shall stand in the same column.

II. Subtract as in subtraction of integers, and place the decimal point before the order of tenths in the remainder.

-

8. $300.25 $75.625; 200.8 miles 150.875 miles.

9. If the minuend is 36 feet, and subtrahend is 20.0025 feet, what is the remainder?

10. From 5 hundred take 5 hundredths. From five thousand and five thousandths take five millionths.

11. I sold a horse for $250, which was $25.75 more than I paid for him. What did he cost me?

12. A housekeeper's bill at a grocer's store was $11.75. What change should she receive from two 10-dollar bills?

13. 2+.002.0008; (300-.03) + (2.99 + .0075)=? 14. To the difference between 5000 and .005 add .00005. 15. A man owed $1000, and paid at one time $300.75, and at another $500.12. What did he then owe?

16. If a pair of horses cost $350.75, and a carriage $175.50, and are all sold for $650.12, what is the gain?

SECTION XVII.

MULTIPLICATION OF DECIMALS.

1. How many ones are 4 ones taken 2 times? Taken 1

3 times? 3 times .2? .4 × 2? taken 2 times? 1 time? 80 × 3? Of .03 × 6?

2. How many tenths are 4 times 2 tenths?
3. How much is 2 times?
4. What is the product of
5. What is the product of
6. What is the product of
7. What is the product of

100

9

30? 10 × 188? 4 x .2?

10

10

X? .05 x .3? 2 x .04?

8. What denominator is produced by multiplying tenths by ones? Hundredths by ones? Tenths by tenths? Tenths by hundredths, or hundredths by tenths?

9. How many ciphers are in the product of the denominators of any two decimal fractions?

10. How many decimal places are in the product of tenths by ones? Hundredths by ones? Tenths by tenths? Tenths by hundredths, or hundredths by tenths?

338. Principle.

The number of decimal places in the product equals the number of decimal places in both factors.