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360.075 kilos may be read as three hundred sixty kilos, and seventy-five grams.

36.15 meters, as thirty-six meters, and fifteen centimeters.

Comparative Table,

An are

3.953 sq.

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.00386 sq.

A sq:

=

A meter
39.37 inches. An inch

.0254 meter.
A meter
3.28 feet. A foot

.3048 meter. A meter = 1.0936 yards. A yard

.9144 meter. A kilometer =.62137 mile.

A mile

1.6093 kilometers A sq. meter = 1550 sq. inches. A sq. inch =.0006452 sq. meter. A sq. meter = 10.76

sq.

feet. A sq. foot = .0929 sq. meter. A sq. meter =

1.196 sq. yards. A sq. yard .8361 sq. meter.
rods. | A

sq.
rod

.2529 are. A hectare = 2.471 acres.

An acre

.4047 hectare. A hectare

mile.
mile =

259 hectares. A liter 33.81 fluid oz. A fluid oz. =

.02958 liter A liter = 1.0567 quarts. A quart

.9465 liter. A liter = .26417 gallon. A gallon

3.786 liters. A hectoliter = 2.837 bushels. A bushel

.3524 hectoliter. A liter = 61.022 cu. inches. A cu. inch = .01639 liter. A hectoliter = 3.531 cu. feet. A cu. foot = .2832 hectoliter. A stere

1.308 cu. yards. A cu. yard .7646 stere. A stere = .2759 cord. A cord

3.625 steres. A gram = 15.432 grains.

A grain A kilogram 35.27 av. ounces. An av. oz. = .0283 kilogram. A kilogram 2.68 Tr. pounds. A Troy lb.

.373 kilogram. A kilogram = 2.2046 av. pounds. An av. Ib.

.4536 kilogram. A tonneau = 1.1023 tons.

A ton

.9071 tonneau.

.0648 gram.

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These equivalents are only determined approximately ; but are sui ficiently exact for all ordinary business.

How many inches make a meter? How many miles a kilometer ? Square inches a square meter ? Square rods an are ? Acres a hectare? Quarts & liter ? Bushels a hectoliter ? Cords a stere? Grains a gram? Pounds Troy a kilo ? Avoirdupois pounds a kilo ? Tons a tonneau? Meters an inch? Kilometers a mile? Square meters a square yard? Ares a square rod ? Hectares an acre ? Liters a quart? Hectoliters a bushel ? Steres a cord? Grams a grain ? Kilograms a pound Troy? Kilograms an avoir dupois pound ? Tonneaux a ton ?

Exercises.

Read

1. 1686.45 2. 537.125 K. 3. 634.56 to 4. 76.7 st. 5. 100.56 ar.

6. 2.006 sq.m.
7. 517.5 HI.
8. 3.1605 Habo
9. 15.1005 ca. m
10. 678.06 L

11. Write in ngures thirty-one hectares and fifteen ares, a: hectares.

12. Write in figures seventeen and five tenths steres.

13. Write in figures sixteen hundred meters and twenty-five centimeters.

14. Express by figures one hundred thirty-two cubic meters, and seven thousand three cubic centimeters.

15. Reduce 8.07018 kilometers to meters.

SOLUTION. Since in 1 kilometer there are 1000 meters, in 8.07018 kilometers there must be 8.07018 times 1000 meters, or 8070.18 meters.

16. Reduce 16.85 grams to kilograms.

Solution. Since in 1000 grams there is 1 kilogram, there are as many kilograms in 16.85 grams as 1000 grams are contained times in 16.85 grams, or .01685 kilogram.

That is, to change from a number of one denomination to an equivalent number of another denomination of the same weight or measure,

we may

Remove the decimal point one or more places to the right or lefth as the case may require, supplying ciphers if necessary.

17. In 560.5 hectares, how many square meters ?
18. In 5605000 square meters, how many hectares ?
19. In .0605 liters, how many centiliters ?
20. In 6.05 centiliters, how many liters ?
21. Express .01531 tonneau as kilograms.

22 Express as millimeters and add, 31.55 meters, 9.005 meders, and 75 millimeters.

Ans. 40630 mm. 23. From 56 hectares take 156 ares.

Ans. 54.44 Ha

How may we change from one denon thation to another of the same weight or measure ?

COMPARISON OF UNITS. 241. The units of the metric and common systems may be readily compared by means of the Comparative Table (Art. 240). 1. In 125 meters how

many

feet? SOLUTION. Since in 1 meter there are 3.28 feet, there will be in 125 meters 125 times 3.28 feet, or 410 feet.

Or, since in 1 foot there are .3048 meter, there will be as many feet in 125 meters, as .3048 meter are contained times in 125 meters, or 410 feet.

2. In 150 acres how many hectares ? 3. In 2.5 hectoliters how

many

bushels ? Ans. 7.09 + bu, 4. In 15 cords how many steres ? Ans. 54.375 steres, 5. Reduce 16.25 kilos to pounds avoirdupois. 6. How many tonneaux in 100 tons ? Ans. 90.71 tonneaux.

CONVERSION OF PRICES OR RATES.

242. When the price or rate per unit is given either in the common or in the metric system, it may be readily found for a corresponding unit in the other system, since

The prices or rates must have the same relation to each other as have the magnitudes of the given units.

1. If the price per kilogram is $.80 cents, what is it per pound ?

SOLUTION. If the price per kilogram is $.80, it must be per pound. which is .4536 times a kilogram, .4536 times $.80, or $.36+: 2. The price per liter being $1, what is it per quart?

Ans. $.946+ 3. The produce per hectare being 10 hectoliters, what is it

Ans. 4.047 hectoliters. 4. The produce per acre being 45 bushels, what is it per hectare?

Ans. 111.195 bushels.

per acre ?

How may the units of the metric and common systems be compared ? To what does the price or rate of units in the different systems correspond ?

DENOMINATE NUMBERS. 243. A Denominate Number is a concrete number expressing weight, measure, or currency. Thus,

5 rods, 3 pounds, 2 ounces, 9 dollars, are each denominate numbers.

A SIMPLE DENOMINATE NUMBER expresses only units of a single denomination of a weight, measure, etc.

A COMPOUND DENOMINATE NUMBER expresses units of two or more denominations of the same kind of weight, measure, etc. Thus,

5 rods 3 yards, 8 pounds 6 ounces, 7 dollars 3 dimes 2 cents, are each compound denominate numbers.

REDUCTION. 244. Reduction of Denominate Numbers is the process of changing their denomination, without changing their value.

CA SE I. 245. To reduce from a higher to a lower denom{nation.

1. Let it be required to reduce 63 lb. O oz. 10 pwt., to pennyweights.

OPERATION.
63 lb. O oz. 10 pwt.
12

Since in 1 pound there are 12 ounces,

in 63 pounds there are 63 times 12 126

ounces, or 756 ounces. 63

Since in 1 ounce there are 20 penny

weights, in 756 ounces there are 756 20

times 20 pennyweights; and 10 penny

weights added, make 15130 penny. 15120

weights. Therefore, etc. 10 15130 pwt., Ans. What is a Denominate Number? A Simple Denominate Number? A Compound Denominate Number? Reduction of Denominate Numbers ?

756 oz.

RULE. Multiply the number of the highest denomination given by the number required of the next lower denomination to make one of that higher, and to the product add the number, if any, of the lower denomination.

Proceed in like manner till the whole is reduced to the required denomination.

Examples. Reduce 2. 3 T. 15 cwt. to pounds.*

6. 583 A. 130 P. to square

rods. 3. 2 lb. 8 oz. to drams.

7. 17 cords to cubic inches. 4. 9 miles to rods.

8. 27 bu. 3 pk. to pints. 5. 98 gal. 1 pt. to pints.

9. 5° 6' 15" to seconds. 10. In 5 fur. 12 rd. 4 yd. how many feet? 11. In 365 d. 5 h. 48 m. 50 sec. how many seconds ? 12. In 24 hhd. 18 gal. 2 qt. how many pints ? 13. In 17 m. 6 fur. 22 rd. 4 yd. 2 ft. 7 in. how many inches ? 14. In 75 bu. 3 pk. 5 qt. how many quarts ? 15. In 4 cwt. 99 lb. 10 oz. 12 dr. how many drams? 16. In 180 degrees how many seconds ?

246. The rule also applies when the denominate number is a common fraction or decimal.

17. Reduce of a gallon to pints.

OPERATION.

# X4=4 qt. ; 4 X 2=24=33 pt. Ans. Since in 1 gallon there are 4 quarts, in & of a gallon there are 4 of 4 quarts, or 12 quarts.

Since in 1 quart there are 2 pints, in * quarts there are 4 of 2 pints, or 44= 34 pints. 18. Reduce te of an acre to square

rods? 19. In of a yard how many quarters ? 20. In 93 days how many minutes ? 21. What part of a pennyweight is 1827 of a pound ?

What is the Rule ?

* For answers, see corresponding examples ir Case II.

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