374.-1. If a block of wood be divided into ten equal parts, what is 1 of the parts called? What are 2 of the parts called? 3 of the parts? 7 of the parts?

2. If one tenth of a block of wood be divided into en equal parts, what is 1 of the parts called? What are 2 of the parts called? 3 of the parts? 7 of the parts? 3. What part of 1 is of? of? of?

4. What part of one tenth is one hundredth? How many hundredths is one tenth?

fo of io?

5. If one hundredth of a block of wood be divided into ten equal parts, what is 1 of the parts called? What are 2 of the parts called? 3 of the parts? 7 of the parts?

6. What part of 1 is of of? of of †? 7. What part of one hundredth is one thousandth? How many thousandths is one hundredth ?

DEFINITIONS.

375. A Decimal Fraction, or Decimal, is a number of tenths, hundredths, thousandths, etc., expressed by placing a point (.) before the numerator and omitting the denominator.

Thus, .3 expresses 3 tenths, or fo; and .03 expresses 3 hundredths, or 180.

376. The point is called the Decimal Point, and in a numerical expression separates the decimal from the order of ones or units.

Thus, 3.003 expresses 3 ones and 3 thousandths, or 3100

377. The first order at the right of the decimal point is tenths, the second hundredths, the third thousandths, etc., as shown in the following

A Mixed Decimal consists of an integer and a decimal.

Thus, 15.165, which is read fifteen ones and one hundred sixtyfive thousandths, or fifteen and one hundred sixty-five thousandths, is a mixed decimal.

378. Principles.-1. Ten of any decimal order are always equal to one of the next higher order.

2. The denominator of a decimal is 1, with as many ciphers annexed as there are orders in the decimal.

SOLUTION.-61.2561 ones and decimal .25;

5 hundredths; or, since .220 hundredths, .25 =

.25 = 2 tenths

= 20 hundreths

+5 hundredths 25 hundredths. Hence, 61.25 is read 61 ones and 25 hundredths; or 61 and 25 hundredths.

3. Write and read .3165.

4. Write and read 515.006.

5. Write three hundred five thousandths.

SOLUTION.-305 thousandths

sandths; 30 hundredths

-

30 hundredths and 5 thou3 tenths and 0 hundredths. Hence,

305 thousandths 3 tenths 0 hundredths 5 thousandths =.305.

6. Write one thousand three hundred thirty-one tenthousandths.

7. Write eleven thousand eleven, and eleven thousandths.

380. Rules for Reading and Writing Decimals.--Read a decimal as though it were an integer, giving it the name of its right-hand order.

Write a decimal as though it were an integer, and place the decimal point so that each figure shall stand in its proper order, marking the absence of units of any order by a cipher.

19. Ninety-eight hundredths.

20. One hundred twenty-five thousandths. 21. One thousand eighteen ten-thousandths.

22. Six, and seventy-five hundredths.

23. Two thousand four hundred sixty-two, and seven tenths.

24. Four hundred, and forty-four thousandths.

25. Twenty-four, and twenty-four millionths.

26. Thirty-five thousand three hundred fifty-one, and twenty-one hundredths.

27. One million two hundred thousand thirty, and one millionth.

SECTION XXXVII.

ADDITION AND SUBTRACTION OF

DECIMALS.

382.-1. What is the sum of 3 tenths and 5 tenths? 2. What is the sum of 7 tenths and 8 tenths?

SOLUTION.-7 tenths and 8 tenths are 15 tenths; and since 10 tenths are equal to 1, 15 tenths are 1 and 5 tenths, or 1.5. Hence, the sum of 7 tenths and 8 tenths is 1.5.

3. What is the sum of 12 hundredths and 11 hundredths?

4. If you pay 25 hundredths of a dollar for a slate, and 10 hundredths of a dollar for some paper, what part of a dollar do you pay for the whole?

5. If you pay 25 hundredths of a dollar for a slate, and 10 hundredths of a dollar for some paper, how much more does the slate cost than the paper?

6. If you have 75 hundredths of a bushel of chestnuts, and your brother has 15 hundredths of a bushel, how many more have you than your brother?

383. Principle.-Decimals which express like parts of a unit may be added or subtracted like integers.

WRITTEN EXERCISES.

384.-1. Add 13.634, 35.423 and 8.56.

13.634

35.423 8.56

57.617

SOLUTION.-Write the numbers so that figures of the same order shall stand in the same column. Add as in addition of integers, which gives 57.617, the result required.

2. Add .315, 17.563 and 63.05.