is — %.

Next read, filling the blanks,

of anything is — % of that thing;

is %; is - %; is - %; is - %.

404. Then practice as directed on page 174, for 16%, 121%, 25%, 331%, 50%, etc. This table will give additional drill on 1%, 10%, 100%, etc.

To drill on other rates % make factors of the above, as 7%; read rapidly 7% is 7 times 1% of 480, or 7 times 4.8; 6% is 6 times 1% of 480, or 6 times 4.8; etc.

For drill in Decimals, read the above as divided by 10, 100, 1000. Thus, by column divided by 10 read 48, 84, 72, 86.4, 64.8, etc.

Read as tenths, etc., of miles, rods, acres, days, etc.

* For the nature and design of this Addenda, see Preface.

ROMAN

ΝΟΤΑΤΙΟΝ.

405. Roman Notation employs seven capital letters

to express numbers. Thus,

D,

M.

X, L, C, 1, 5, 10, 50, 100, 500, 1000.

Letters. I,
Values.

All other numbers may be expressed by combining these letters according to the following

PRINCIPLES.

I. Repeating a letter repeats its value.

Thus, XX represents 20, CCC, 300; DD, 1000.

II. When a letter is placed after one of greater value, its value is to be added to that of the greater.

Thus, VI represents 6; XV. 15; LXX, 70; DC, 600.

III. When a letter is placed before one of greater value, its value is to be taken from that of the greater.

Thus, IV represents 4; IX, 9; XL, 40; XC, 90.

IV. When two or more letters, each of a less value, are placed after one of greater value, their values are to be added to that of the greater.

Thus, XIV represents 14; LIX, 59; CXL, 140.

V. A bar or dash placed over a letter increases its value one thousand times.

Thus, X represents 10000; XC, 90000; DL, 550000.

Express by Roman notation:

CIRCULATING DECIMALS.

406. When the numerator of a fraction, with ciphers annexed, is exactly divisible by the denominator, the result is called a perfect decimal.

Thus, equals .25, and equals .375 are perfect decimals.

40%. A circulating decimal is a decimal in which a figure, or set of figures, is repeated in the same order; and the figure, or set of figures repeated, is called the repetend. Thus, equals .333+ and equals .7272 are circulating decimals, and the 3 and 72 are the repetends.

408. A repetend is written but once, and a point (.) is placed over the single figure, or over the first and last of the set of figures.

Thus, .555 and .135135 are written .5 and .135.

PRINCIPLE. Every fraction whose denominator, in its lowest terms, contains other prime factors than 2 or 5 is equivalent to a circulating decimal.

A pure circulating decimal is a decimal which commences with a repetend; as .7, or .279.

A mixed circulating decimal is a decimal in which the repetend is preceded by one or more decimal places called the finite part of the decimal; as, .27, or .04648, in which .2 or .04 is called the finite part.

409. To change a fraction to a perfect or circulating decimal.

Change

1. To perfect decimals, 3, 2, 18, 48, 14, and

.

2. To pure circulating decimals, 4, J. 1, 14, 11, and 4. 3. To mixed circulating decimals, fe, f, H, I, and 1.

The law for the formation of repetends will be apparent from the following:

1..1111+

=.i.

5..4444+

3.

2. .01010+ =.01. 6. =.2323+ 3..001001+ =.001. 7. 335 =.135135+

4. .00010001+.0001. s. 188.17281728+=.1728.

=

PRINCIPLE-A repetend is changed to the form of a fraction by writing for a denominator as many NINES as there are figures in the repelend.

410. To change a circulating decimal to the form of a fraction.

1. Change .216 to the form of a fraction.

In like manner, change to the form of fractions:

10. Change 2.297 and 12.081 to the form of improper frac

tions.

11. Change .227 to the form of a fraction.

In like manner, change to the form of fractions or mixed numbers:

To add, subtract, multiply, or divide circulating decimals, reduce them

to fractions, and then perform the required operation.

A knot, used in measuring distances at sea, is equivalent to a nautical mile.

415. Apothecaries' fluid measure is used in prescribing and in compounding liquid medicines.

1. O stands for the Latin Octarius, a Pint; C, for Congius, a Gallon. A common teaspoonful, or 45 drops, makes about one fluidrachm. A common tablespoon holds about half a fluid ounce.

B is an abbreviation for recipe, or take; ā, aa, for equal quantities; j. for 1; ij. for 2; ss. for semi, or half; gr for grain; P for a little part; P. æq. for equal parts, q. p., as much as you please; gtt. for drops.