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DECIMAL ARITHMETIC is the most simple and explicit mode of performing practical calculations; on account of its doing away with the necessity of fractional parts in the fractional form, thereby reducing long and tedious operations to a few figures, arranged and worked in all respects according to the usual rules of common arithmetic.
Decimals simply signify tenths: thus, the decimal of a foot is the tenth part of a foot, the decimal of that tenth is the hundredth of a foot, the decimal of that hundredth is the thousandth of a foot, and so might the divisions be carried on and lessened to infinity; but in practice it is seldom necessary to take into account any degree of less measure than a onehundredth part of the integer or whole number. And, as the entire system consists in supposing the whole number divided into tenths, hundredths, thousandths, &c., no peculiarity of notation is required, otherwise than placing a mark or dot, to distinguish between the whole and any part of the whole: thus 34.25 gallons signify 34 gallons 2 tenths and 5 hundredths of a gallon; 11.04 yards signify 11 yards and 4 hundredths of a yard; 16·008 shillings signify 16 shillings and 8 thousandth parts of a shilling: from which it must appear plain, that ciphers on the right hand of decimals are of no value whatever; but placed on the left hand, they diminish the decimal value in a tenfold proportion, for 6 signifies 6 tenths; '06 signifies 6 hundredths; and '006 signifies 6 thousandths, of the integer or whole number.
Reduction means the construing or changing of
vulgar fractions to decimals of equal value; also finding the fractional value of any decimal given.
Rule 1. Add to the numerator of the fraction any number of ciphers at pleasure, divide the sum by the denominator, and the quotient is the decimal of equivalent value.
Rule 2. Multiply the given decimal by the various fractional denominations of the integer or whole number, cutting off from the right hand of each product for decimals a number of figures equal to the given number of decimals, and thus proceed until the lowest degree, or required value, is obtained.
Ex. 1. Required the decimal equivalent, or decimal of equal value, to of a foot.
Ex. 2. Reduce the fraction of an inch to a decimal of equal value.
Ex. 3. What is the decimal equivalent to of a gallon?
Ex. 4. Required the value of the decimal 40625 of an inch.
1.000003 and of an inch, the value required.
Ex. 5. What is the value of 625 of a cwt.?
14.000 2 quarters and 14 tbs., the value required.
Ex. 6. Ascertain the value of 875 of an imperial
1.0003 quarts and 1 pint, the value required.
Ex. 7. What is the value of 525 of a £. sterling?
6.00010 shillings and 6 pence, the value required.
Independent of the mark or dot which distinguishes between integers and decimals, the fundamental rules, viz., Addition, Subtraction, Multiplication, and Division, are in all respects the same as in Simple Arithmetic; and an example in each, illustrative of placing the separating point, will no doubt render the whole system sufficiently intelligible, even to the dullest capacity.