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PROB. II.

To find the Value of a decimal Fraction, in the

known Parts of the Integer.

Multiply the decimal proposed into the number of equal parts contained in the integer, and the product will be the number of such parts as are expressed by by the fraction. What is the value of .25 of a pound sterling?

20

Answer shillings 5.00

For .25 or o of one pound, is equal to the one hundredth part of 25 pounds, or of the shillings in 25 pounds, which are 500; therefore the one hundredth part thereof will be 5 shillings; which is effected by cutting off the two cyphers, for the two decimals, by a point.

What is the value of .385 of a pound sterling ?

| 20

Shillings 7.700

12

Pence 8.400

Farthings 1.600

What is the value of 48 of a chain of 50 links?

50

Answer links 24.00

What is the value of .2864 of a shilling?

12

Pence 34.368

4

Farthings 1.7472
What is the value of .287 of a pound weight troy?

Oz. dwt. gr.
Answer 38 8 21

What is the value of .2945 of a pound avoirdapoise ?

Oz. dwts.
Answer 4 111.

THE EXTRACTION OF THE SQUARE ROOT.

A SQUARE number is the product of a number multiplied by itself; and the number so multiplied, is called the root of that square ; thus 9 is the square of 3, and 3 is the root of 9, for 3 multiplied by 3 is 9.

If a square number be given to find its root, observe

be odd or even, if they be odd, find the root of the first figure; but if they be even, of the two first; un- . der which place the square of that root, and deduct, placing the root in the quotient, and bring down two figures to the remainder.

Let the double of the said root be made a divisor to all the figures of that last remainder, except the last; put the quotient thereof with the root, or former quotient; and having multiplied it into the numbers so formed, deduct the product from the foregoing figures or resolvend, and in like manner proceed, till all the figures of the given square are exhausted.

If there be any decimals in the given square, their number must be even, or made so, before we begin to find the root, by adding a cypher to the right hand; and for every two places of decimals in the square, let one be cut off in the root,

EXAMPLES,

1. What is the square root of this square number, 298116?

29,8 1,16 (54 29,81,16(546

25 25

i og

1481
416

104)481

416

J65th

1086).6516

6516

6514 28,72,18 (5 2 $

377

ها و

Henrhm 23

Because the number of figures in the given square number is even, we find the nearest square number to the two first figures 29, which is 25, the root whereof 5, we set in the quotient, and deduct 25 from 29, and to the residue 4, we annex the following figures, 81, so'we have 481, for a resolvend.

The double of the first figure in the quotient being 10, is then set as a divisor to 48, all the figures in the resolvend, but the last ; and finding it to be contained 4 times, we annex the 4 to the divisor and quotient; the then divisor, 104, is multiplied by the last figure in the quotient, 4, and the product 416 is deducted from the resolvend 481, to the residue whereof is annexed the two following figures in the square, so we have 6516 for a new resolvend, to all which figures but the last we make 108, the double of 54, the figures in the quotient a divisor, and finding it will be contained 6 times, we place 6 in the divisor and quotient; the then divisor 1086 is multiplied by the last figure in the quotient 6, and the product being set under the resolvend and thence deducted, leaves nothing; so is 546 the root sought.

For if the root 546 be squared or multiplied by 546, the product will be the square number given.

546

25

Siznana Monsilna 298116 (546 quolirne in 104) 4 8 1 nevoland

5 46 squared rinin 108 665 16

416

6.516

5*40
3276

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Here being an odd decimal figure, we annex any odd number of cyphers to make the decimal places even; and then extracting the root as before, we thence cut off half the number of decimals that we have in the square. Thus,

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