NOTE. If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c.

NUMERATION OF DECIMAL FRACTIONS.

Let the pupil write the following numbers.

1. Three hundred seven, twenty-five hundredths. 2. Forty-seven, and seven tenths.

3. Eighteen and five hundredths.

4. Twenty-nine and three thousandths. 5. Forty-nine ten thousandths.

6. Eight and eight millionths.

7. Seventy-five and nine tenths.

8. Two thousand and two thousandths.

9. Eighteen and eighteen thousandths.

10. Five hundred five, and one thousand six millionths.

Section 27.

ADDITION OF DECIMALS.

1. Add together 5.018; 171,16; 88.133; 1113.6; .00456, and 14.178.

OPERATION.

5.018 171.16

88.133

1113.6

.00456

14.178 1392.09356=

Five and eighteen thousandths.

One hundred seventy-one, sixteen hundredths.
Eighty-eight, and one hundred thirty-three thousandths,
One thousand one hundred thirteen, and six tenths.
Four hundred fifty-six hundred thousandths.

Fourteen, and one hundred seventy-eight thousandths.
One thousand three hundred ninety-two, and nine
thousand three hundred fifty-six hundred thousandths.

RULE.

Write the numbers under each other according to their value, add as in whole numbers, and point off from the right hand as many places for decimals, as there are in that number, which contains the greatest number of decimals.

J

Ans. 260.489775.

2. Add together 171.61111; 16.7101; .00007; 71.0006, and 1.167895. 3. Add together .16711; 1.766; 76111.1; 167.1; .000007, and 1476.1. Ans. 77756.233117.

4. Add together 151.01; 611111.01; 16.5; 6.7; 46.1, and .67896. Ans. 611331.99896. 5. Add fifty-six thousand and fourteen thousandths, nineteen and nineteen hundredths, fifty-seven and forty-eight ten thousandths, twenty-three thousand and five and four tenths, and fourteen millionths. Ans. 79081.608814. 6. What is the sum of forty-nine and one hundred and five ten thousandths, eighty-nine and one hundred seven thousandths, one hundred and twenty-seven millionths, forty-eight ten thousandths ? Ans. 138.122427. 7. What is the sum of three and eighteen ten thousandths, one thousand five and twenty-three thousand forty-three millionths, eighty-seven and one hundred seven thousandths, forty-nine ten thousandths, and forty-seven thousand and three hundred nine hundred thousandths? Ans. 48095:139833.

Section 28.

SUBTRACTION OF DECIMALS.

RULE.

Let the numbers be so written that the separatrix of the subtrahend be directly under that of the minuend, that is, units under units, and tens under tens, &c.; subtract as in whole numbers, and point off so many places for decimals, as there are in that number, which contains the greatest number of decimals.

Ans. 99.999.

9. From 100. take .001. 10. From seventy-three take seventy-three thousandths.

Ans. 72.927.

11. From three hundred sixty-five take forty-seven ten

Ans. 364.9953.

thousandths. 12. From three hundred fifty-seven thousand take twentyeight and four thousand nine ten millionths. Ans. 356971.9995991.

Hence, we deduce the following

RULE.

Multiply as in whole numbers, and point off as many figures for decimals in the product, as there are decimals in the multiplicand and multiplier; but, if there be not so many figures in the product, as in the multiplicand and multiplier, supply the defect by prefixing ciphers.

Ans..12649. Ans. 18.58922, Ans. .00000114.

Ans. 1137. Ans. 2.20947. Ans. .00046967. Ans. 22.09.

3. Multiply 18.07 by .007. 4. Multiply 18.46 by 1.007. 5. Multiply .00076 by .0015. 6. Multiply 11.37 by 100. 7. Multiply 47.01 by .047. 8. Multiply .0701 by. 0067. 9. Multiply 47. by .47. 10. Multiply eighty-seven thousandths by fifteen millionths. Ans. .000001305. 11. Multiply one hundred seven thousand and fifteen ten thousandths by one hundred seven ten thousandths. Ans. 1144.90001605. 12. Multiply ninety-seven ten thousandths by four hundred and sixty-seven hundredths. Ans. 3.886499. 13. Multiply ninety-six thousandths by ninety-six hundred thousandths. Ans. .00009216. 14. Multiply one million by one millionth. Ans. 1. 15. Multiply one hundred by fourteen ten thousandths.

Ans. .14. 16. Multiply one hundred and one thousandth by ten thousand one hundred one hundred thousandths.

Ans. .01020201. 17. Multiply one thousand fifty and seven ten thousandths, by three hundred five hundred thousandths.

Ans. 3.202502135.

18. Multiply two million by seven tenths.

Ans. 1400000.

19. Multiply four hundred and four thousandths by thirty and three hundredths. Ans. 12012.12012. 20. What cost 46lbs tea at $ 1.125 per lb. ? $51.75. 21. What cost 17.125 tons of hay at $18.875 per ton?

Ans. $323.234375.

22. What cost 18lbs. sugar at $.125 per lb. ?

Ans. $2.25.

Divide as in whole numbers, and point off as many decimals in the quotient, as the number of decimals in the dividend exceed those of the divisor; but, if the number of those in the divisor exceed that of the dividend, reduce the dividend to the same denomination as the divisor by annexing ciphers. And, if the number of decimals in the quotient and divisor together are not equal to the number in the dividend, supply the defect by prefixing ciphers to the quotient.

15. Divide one hundred forty-seven and eight hundred

twenty-eight thousandths by nine and seven tenths.

Ans. 15.24.