REVIEW AND TEST QUESTIONS.

365. 1. Define Decimal Unit, Decimal Fraction, Repetend, Circulating Decimal, Mixed Circulating Decimal, Finite Decimal, and Complex Decimal.

2. In how many ways may be expressed as a decimal fraction, and why?

3. What effect have ciphers written at the left of an integer? At the left of a decimal, and why in each case (316)? 4. Show that each figure in the numerator of a decimal represents a distinct order of decimal units (320).

5. How are integral orders and decimal orders each related to the units (323)? Illustrate your answer by lines or objects.

6. Why in reading a decimal is the lowest order the only one named? Illustrate by examples (321).

7. Give reasons for not regarding the ciphers at the left in reading the numerator of the decimal .000403.

8. Reduce to a decimal, and give a reason for each step in the process.

125

9. When expressed decimally, how many places must 13 give, and why? How many must give, and why?

10. Illustrate by an example the reason why cannot be expressed as a simple decimal (327).

11. State what fractions can and what fractions cannot be expressed as simple decimals (326 and 327). Illustrate by examples.

12. In reducing to a complex decimal, why must the numerator 5 recur as a remainder (328-1 and 2)?

13. Show that, according to (235-II and III), the value of will not be changed if we diminish the numerator and denominator each by of itself.

14. Show that multiplying 9 by 1 increases the 9 by of itself,

15. Multiplying the numerator and denominator of each by 1 produces what change in the fraction, and why?

16. Show that in diminishing the numerator of by and the denominator by 1 we diminish each by the same part of itself.

17. In taking .3 as the value of, what fraction has been rejected from the numerator? What must be rejected from the denominator to make .3, and why?

18. Show that the true value of .81 is §. Give a reason for each step.

19. Explain the process of reducing a mixed circulating decimal to a fraction. Give a reason for each step.

20. How much is .33333 less than 1, and why?

21. How much is .571428 less than 4, and why?

22. Find the sum of .73, .0049, .089, 6.58, and 9.08703, and explain each step in the process (261—I and II).

23. If tenths are multiplied by hundredths, how many decimal places will there be in the product, and why (355) ?

24. Show that a number is multiplied by 10 by moving the decimal point one place to the right; by 100 by moving it two places; by 1000 three places, and so on.

25. State a rule for pointing off the decimal places in the product of two decimals. Illustrate by an example, and give reasons for your rule.

26. Multiply 385.23 by .742, multiplying first by the 4 hundredths, then by the 7 tenths, and last by the 2 thousandths. 27. Why is the quotient of an integer divided by a proper fraction greater than the dividend?

28. Show that a number is divided by 10 by moving the decimal point one place to the left; by 100 by moving it two places; by 1000, three places; by 10000, four places, and so on.

29. Divide 4.9 by 1.305, and give a reason for each step in the process. Carry the decimal to three places.

30. Give a rule for division of decimals.

DENOMINATE NUMBERS

DEFINITIONS.

366. A Related Unit is a unit which has an invariable relation to one or more other units.

Thus, 1 foot 12 inches, or of a yard; hence, 1 foot has an invariable relation to the units inch and yard, and is therefore a related unit.

367. A Denominate Number is a concrete number (15) whose unit (14) is a related unit.

Thus, 17 yards is a denominate number, because its unit, yard, has an invariable relation to the units foot and inch, 1 yard making always 3 feet or 36 inches.

368. A Denominate Fraction is a fraction of a related unit.

Thus, of a yard is a denominate fraction.

369. The Orders of related units are called Denominations.

Thus, yards, feet, and inches are denominations of length; dollars, dimes, and cents are denominations of money.

370. A Compound Number consists of several numbers expressing related denominations, written together in the order of the relation of their units, and read as one number. Thus, 23 yd. 2 ft. 9 in. is a compound number.

371. A Standard Unit is a unit established by law or custom, from which other units of the same kind are derived.

Thus, the standard unit of measures of extension is the yard. By dividing the yard into 3 equal parts, we obtain the unit foot; into 36 equal parts, we obtain the unit inch; multiplying it by 5, we obtain the unit rod, and so on.

372. Related units may be classified into six kinds :

373. Reduction of Denominate Numbers is the process of changing their denomination without altering their value.

UNITS OF WEIGHT.

374. The Troy pound of the mint is the Standard Unit of weight.

16 0%. = 1 lb. 100 lb. = 1 cwt.

20 cwt.

1 T

1. Denominations.

Ounces (oz.),

pounds (b), hundredweights (cut.), tons (T.). 2. Equivalents.-1 Ton 20 cwt. = 2000 lb. 32000 oz.

3. Use.-Used in weighing groceries, drugs at wholesale, and all coarse and heavy articles.

4. In the United States Custom House, and in wholesale transactions in coal and iron, 1 quarter = 28 lbs., 1 cwt. = 112 lb., 1 T. = 2240 lb. This is usually called the Long Ton table.

APOTHECARIES' WEIGHT.

TABLE OF UNITS.

20 gr. = 1 sc. or . 301 dr. or 3. 83 = 1 oz. or

12 oz. 1 lb.

=

2. Equivalents.

288 gr. 5760.

3. Use.-Used in medical prescriptions. 4. Medical prescriptions are usually

written in Roman notation. The number is written after the symbol, and the final "i" is always written j. Thus, 3 vij is 7 ounces.

Table of Avoirdupois Pounds in a Bushel, as Established by Law in the States named.

Peas, Beans, and Potatoes are usually weighed 60 lb. to the bushel.