0.1234 is read one thousand two hundred and thirty

four ten thousandths.

four and three tenths.

thirty-seven and three tenths.

three hundred and sixty-five and three hundredths.

A number composed of a whole number and a decimal part, is called a mixed number.

?

What is a decimal fraction? Of what form is the denominator? Give examples of decimal fractions. In practice, which part is not written, but understood? What purpose does the decimal point serve? What place is the first figure on the right of the decimal point said to occupy? What place does the second figure occupy What place does the third figure occupy? In what ratio do the values decrease in passing to the right? Is the above table in accordance with the French or English method of notation? Does annexing a cipher to a decimal alter its value? What effect is produced by prefixing a cipher? A number which is composed of a whole number and decimal is called, what?

Let the pupil be exercised in decompounding decimals, as we have done in the following

EXAMPLES.

The expression, 7468, implies that 7468 is to be divided by 1000. Performing the division by the method of CASE IV, ART. 30, we obtain 7 for a quotient and 468 for a remainder. So that 1468-746-7-468-7 units, 4 tenths, 6 hundredths, 8 thousandths, or, which is the same thing, it equals 7+ + 180+ TOOO.

100

364587-364587-36458+. 364587-3645-87-3645+ + +0. 394587-364-587-364+1+180+ 1000. 364587-36-4587-36++OUT TOOO+ Toooo. 364587-3-64587=3+1+oot Toout To Boot

1000

10000

100000

50. SINCE decimals, like whole numbers, increase from the right towards the left, they may be treated by the same rules as for whole numbers, provided we are careful to keep the decimal point in the right place, so that like orders may stand under each other. Hence we have this

RULE.

Place the numbers so that the decimal points shall be directly under each other; add as in whole numbers. In the amount place the point under the points in the numbers added.

How do you place the numbers to be added? How, the point in the amount !

6. What is the sum of 0.123, 0·012, 0-675, 0·0045?

Ans. 0-8145.

Ans. 1:1718.

7. What is the sum of 0.14145, 0-23235, 0-34345, 0.45455 ? 8. Find the sum of 1.0012, 231003, 101-31407, 10:101578. Ans. 135.517148.

9. Find the sum of 234-12, 23-412, 2·3412, 0·23412 Ans. 260.10732.

10. What is the sum of 111-111, 12-1212, 13-1313, 14-1414?

Ans. 150.5049.

SUBTRACTION OF DECIMAL FRACTIONS.

51. There is no difference between the subtraction of decimals and that of whole numbers, provided we are careful to keep the decimal points directly under each other, so that like orders may stand under each other. Hence this

RULE.

Place the less number under the greater, so that the decimal points shall be directly under each other; subtract, as in whole numbers. In the difference place the point under the points of the numbers above.

How do you place the numbers in subtraction? Then how do you proceed?

MULTIPLICATION OF DECIMAL FRACTIONS.

52. A tenth taken once, must give 1 tenth for a product; if taken only one-tenth of a time, the product will be one-tenth of a tenth, or one hundredth; that is, x To, or decimally expressed 0.1x01-001. This is evidently true, since if the tenth-part of any thing be divided into 10 equal parts, each subdivision will be a hundredth-part of the whole. So of 10, and so on.

Multiply 0.136 by 0.78. If we supply the denominators of these decimal fractions, which denominators are always understood, we shall have

78

Hence, multiplying 13 by 7, (ART. 45,) we find

1000

From which we see that the number of decimal places in the product, always denoted by the number of zeros in the denominator, which is understood, is equal to the number of decimal places in both factors. Hence we have this

RULE.

Multiply as in whole numbers, and give as many decimal places in the product as there are in both the factors. When there are not as many places in the product, prefix ciphers.

How do you multiply decimals? How many decimal places must there be in the product? When the whole number of figures in the product is not as great, how do you proceed?