The practical arithmetic

2. An Infinite Decimal is one which does not terminate, and has plus generally placed at the end of it, as 78539 +

3. A repeating Decimal, or repetend, is when one, two, or more figures continually repeat, as .3333, &c., which is called a single repetend, and is generally written thus, .3

Also, .454545 &c. = .45

and .267267 &c. = .267; and so on, which are compound repetends.

Again, .41333 &c. = .413, and 4.21666 &c. 4-216, are compound or mixed repetends, having significant figures between the repetend and decimal point, or a whole number before the repetend.

ADDITION OF DECIMALS.

RULE.-Place the figures in such order, that those of the same denominations may stand under each other; add them together as in whole numbers, and place the decimal point in the sum under the other points.

EXAMPLES.

1. Add 3.45; 46.789; .4689; 468.7 and .25 together.

3.45 46.789

.4689

468.7

.25

519.6579

2. Add 4.37; 56.785; .3724; 865.72; 467.846; and .72 together. Ans. 1395.8134. 3. Add .34; .867; .4956; .78546; 2.68; and 378.42

together.

4. Add .37; .4689; .5; .864; 23; together.

5. Add 3.67; .056; 46.7234; 634.8;

Ans. 383.58806 785; and 745.8 Ans. 1556.0029, and .78 together.

Ans. 686.0294.

6. Add .4; .05; .006; .0007; .00008; and .000009

together.

Ans. .456789.

SUBTRACTION OF DECIMALS.

RULE. Place the numbers in such order, that the decimal point in the greater number may be over the decimal point in the less, and proceed as in Simple Subtraction, placing the point in the difference under the other points.

5. Required the sum and difference of 24.698 and 39.12345. Ans. 63.82145 sum, 14.42545 difference. 6. What number added to .7854 will make 2? Ans. 1.2146.

MULTIPLICATION OF DECIMALS.

RULE.-Place the given numbers as in Simple Multiplication, and find their product.

Point off as many figures, from right to left, in the product, for decimal places, as there are decimals in both the multiplier and multiplicand.

If there be not as many figures in the product as there are decimal places in the multiplier and multiplicand, make up the deficiency by annexing ciphers to the left of the product, as in Example 2nd.

EXAMPLES.

3. Multiply 46.784 by 3.65
4. Multiply 7.3284 by .049
5. Multiply 75.6842 by 3.678
6. Multiply .84623 by 42.5
7. Multiply .004 by 0004
8. Multiply 3.467 by 4.69

Ans. 170.7616. Ans. .3590916 Ans. 278.3664876. Ans. 35.964775. Ans. .0000016.

Ans. 16.26023.

9. Required the sum, difference, and product, of 4.56 and 3.5 Ans. 8.06 sum, 1.06 diff. 15.96 prod. 10. Find the sum, difference, and product, of .06 and .428571 Ans. .488571 sum, .368571 diff. and .02571426 prod.

DIVISION OF DECIMALS.

RULE.-1. Divide as in whole numbers, and point off as as many decimal places in the quotient as the decimal places in the dividend exceed those in the divisor. See Example 1st.

2. If the quotient have not so many places of figures in it, as there are decimal places in the dividend more than the divisor, add ciphers to the left of the quotient, to make up the deficiency, as in Example 2nd.

3 If the divisor contain more figures than the dividend, add as many ciphers to it as may be required in order to perform the division, as in Example 3rd.

4. If there be not as many decimal places in the dividend as in the divisor, make the decimal places equal by annexing ciphers, as in Example 4th.

5 If there be a remainder after division, ciphers may be added to the right of it, and proceed with the division. These ciphers are decimals. If the dividend be a repetend, the repeating figures must be added instead of ciphers, as in Example 5th.

EXAMPLES.

15. Express the quotient of 1694 .647 by 46.849.

Ans. 36.172546

16. What is the sum, difference, product, and quotient, of .0469 and 1.2? Ans. 1.2469 sum, 1.1531 difference, .05628 product, .039083 or 25.58 + quotient.

REDUCTION OF DECIMALS.

CASE I. To reduce a given vulgar fraction to a decimal, of the same value.

RULE.-Divide the numerator, with as many ciphers annexed to the right of it for decimals, as may be required to perform the division; and point of the decimal places in the quotient as in division.

NOTE. When the quotient becomes a repetend, if a single one, place a dot over the repeated figure; if a compound one, place dots over the first and last figures of the repetend, as in Example 2nd.

EXAMPLES.

1. Reduce,, and to decimals of the same value.