NUMERATION OF DECIMALS.

ART. 42. In reading a decimal expressed in figures, two things are necessary: 1st. To ascertain what the figures express as a whole number. 2d. To ascertain the order of the right hand figure. In a whole number, the right hand figure is always units. In a decimal, it is found by commencing at the decimal point and naming each order toward the right. Ex. 1. Express in words .002015607.

Explanation.-Commence at the right hand and separate the figures into periods as in whole numbers, thus: 2.015.607. Next commence at the decimal point and name the orders to the last decimal figure, which is billionths. Then read the decimal as a whole number, adding the name of the last decimal figure, thus: two millions, fifteen thousand, six hundred and seven billionths. Hence the following general

RULE.

Read the figures as in whole numbers and add the name of the last decimal order.

Suggestion.-Read the whole number as units, and then

the decimal.

6. 7080.00607008

7. .002005505

8. .006

9. 600.06

10. 1000.001

11. 25000000.000250

12. 206.000000206

NOTATION OF DECIMALS.

ART. 43. Ex. 1. Express in figures ten thousand five hundred and five millionths.

Explanation.-Write the numerator of the decimal as a whole number, thus: 10505. Then place the decimal point so that the right hand figure may be millionths, filling up the vacant order with a cipher, thus: 010505.

RULE.

Write the decimal as a whole number, and place the decimal point so that the right hand figure shall be of the same name as the decimal.

Express in figures:

Examples.

1. Twenty-five thousandths. 2. Twenty-five millionths.

3. Twenty-five hundredths.

4. Two hundred and five ten-thousandths.

5. Two hundred and five ten-millionths.

6. Twenty thousand and five millionths.
7. Two thousand and four ten-thousandths.

8. Six hundred and fifty units and thirty-seven thousandths.

9. One unit and one millionth.

10. Five thousand units and five thousandths.

11. Two thousand five hundred and six hundredths.. Note.-The above is an improper decimal. The point falls between the figures, thus:,25.06.

12. Nine millions, fifteen thousand, and twenty-five millionths.

13. Eight thousand and forty ten millionths.

14. One million and one millionths.

REDUCTION OF DECIMALS.

ART. 44. A whole number may be changed to a mixed decimal, or a decimal to an equivalent decimal of a lower order by annexing ciphers. Thus: .025 .025000, and 325.=325.000. This is, in effect, multiplying both terms of a fraction by the same number.

A mixed decimal may be reduced to an improper decimal fraction by removing the decimal point and writing the denominator, thus: 205.025-2002. The following examples will make the student familiar with these changes:

Ans, 400. Ans. 500. Ans. 62304. Ans. 36030400.

13. Reduce 4.506 to billionths.
14. How many tenths in 40 units?
15. How many millionths in 5 thousandths?
16. How many thousandths in 62.304 ?
17. How many millionths in 36.0304?
18. How many hundredths in 400 ?
19. How many tenths in 6 tens?

20. How many millionths in one million?

Ans, 40000.

ART. 45. To reduce a decimal to an equivalent common fraction.

Ex. Reduce 25 to an equivalent common fraction.

25. Ans.

RULE.

Supply the denominator, and reduce the fraction to its lowest terms.

ART. 46. To reduce common fractions to an equivalent

decimal.

Ex. Reduce to a decimal.

4)3.00

.75 Ans.

Explanation. of 3; but 3=3.00, hence of 3.00

=.75.

RULE.

Annex ciphers to the numerator and divide by the denominator. Point off as many decimal places as there are annexed ciphers.

ADDITION OF DECIMALS

ART. 47. Ex. 1. Add 6.025, 65.37, 100.0035, and .875.

6.025

65.37

100.0035

.875

172,2735 Ans.

Explanation.-Since decimals are written

upon the same scale as whole numbers, they are added in the same manner.

RULE.

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

Add as in whole numbers, and point off in the result as many decimal places as are equal the greatest number found in any of the numbers added.

Note. The decimal points of the several decimals added and of the answer stand in the same column.

Examples.

Ex. 2. Add .37, .02561, .00015, .5, .271, and .026.

3. What is the sum of 256 thousandths, 3005 millionths, 207 ten-thousandths, 45 hundred-thousandths, 7 hundredths, and 20037 millionths?

4. Add .00675, 4,5689, 3.00007, 2.05, 3.68003, .9375, 8.75, 6.4375.

5. What is the sum of 307 millionths, 56 ten-thousandths, 683 hundredths, 5 hundred-thousandths, 256 tenths, 18 tenmillionths, and 25 hundredths? Ans. 26.568483875.

6. Add 375 ten-thousandths, 375 thousandths, 375 hundredths, 375 tenths, and 375 units. Ans. 416.6625.

7. A man bought 4 barrels of molasses, each containing