EXAMPLE II.

Divide 574 34782 by 6134775, and retain two places of decimals in the quotient.

In this Example, the units place in the product falls under the third place of integers in the dividend, therefore you will have three places of integers in the quotient; consequently you must cut off five places from the divisor, in order to have two places of decimals.

EXAMPLE III.

Divide 75.434748 by 61377.5, and preserve four places in the quotient, besides the prefixed ciphers.

In the last Example, because the units place in the product stands under the third place of decimals, therefore I prefix two ciphers, which makes the first quotient figure out to three places of decimals, and proceed as in the former Example.

PROBLEM V.

To reduce a vulgar fraction to a decimal fraction.

Add ciphers at pleasure to the numerator of decimal places, and divide by the denominator as far as it is necessary, as in division of decimals.

To reduce the known parts of any integer to a decimal fraction.

I. Begin at the lowest denomination, and divide it by as many as will make one of the next superior denomination, and add to the quotient the next superior denomination, if any, of the given integer.

II. Proceed in this manner to the highest place, observing to point out the decimal parts at each operation, and you

will have the answer.

VOL. I.

S

EX

EXAMPLE I.

Reduce 15s. 9 d. to the decimal of a shilling.

Reduce 14s. 6d. to the decimal of u pound.

12)6'0 2,0)14'5,0

Ans. 725

EXAMPLE III.

Reduce 2ft. 3in. to the decimal of a foot.

12)3.00

Ans. 2:25

PROBLEM VII.

To reduce a decimal to the known parts of an

integer.

I. Multiply the decimal by the next inferior denomination, and cut off the decimal parts.

II. Multiply the decimal parts by the next inferior denomination, cut off the decimals as before, proceed in this manner to the lowest denomination, and the parts on the 4t hand of the decimals will be the answer.

EXAMPLE I.

What is the known parts of 725 of a pound sterling?

7.25

20

14.500

12

6:0

Ans. 14s. 6d.

EXAMPLE II.

What is the value of 225 of a foot?

2.25

12

3.00

Ans. 2ft. 3in.

I shall here end decimal arithmetic, and show its application more particularly to mensuration; as my design in this book is not to write a book of arithmetic, but only to explain the most useful rules, that the artist may have every possible advantage in its application, as it may sometimes. fall in his way.