ROMAN NOTATION

1. What is meant by Roman notation?

2. Why is it so called? It is little used now.

some of its uses.

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Name

The numerals with which we write numbers are called Arabic or Hindu numerals, because the Hindus invented them and the Arabs introduced them into Europe.

3. Write the Roman symbols as usually seen on clock faces.

4. Write in Roman numerals the numbers from 10 to 50. 5. For what numbers do the following letters stand: I, V, X, L?

The symbol for 100 is C, for 500 is D,

and for 1,000 is M.

Thus, CCXL means in modern notation 240;

DCCIX means in modern notation 709;

MDCCC means in modern notation 1,800.

6. What number does V represent? IV is how many less than V?

7. What number does X represent? IX is how many less than X?

8. What number does L represent? XL is how many less than L?

9. Similarly CD is 100 less than D. Read CD; CDXIX. 10. CM is how many less than M? Read CMIV; MCMIV. II. Write in Roman notation 1904; 1900; 1899; 1892. 12. Write in Roman notation the number of the year in which Columbus discovered America.

13. Write in Roman notation the number of the present year.

14. If convenient, bring some book which has chapter numbers in Roman numerals and read them.

15. Make and solve other problems like Exercise 12.

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PROBLEMS-NATURE STUDY

1. Fasten a small piece of lead or clay to a string and suspend from a hook or nail, as shown in the picture. Ad

just it so that the string may move freely. Such an instrument is called a pendulum. Make the string 2 ft. long, set the ball swinging and count the number of swings in 1 minute.

2. Calculate the number of swings the pendulum would make if it continued

to swing at the same rate for 1 hour; for 24 hours.

3. Make a similar observation with a pendulum 21 ft. long. Calculate the number of swings for 1 hour; for 1 day.

4. Make a similar observation with a pendulum 3 ft. long; 4 ft. long. Calculate the number of swings of each for 1 hour; for 1 day.

5. Dean saw the steam when a mill-whistle blew and observed that the sound reached him 5 seconds after he saw the steam. The velocity of sound is 1,090 ft. per second. How far was Dean from the mill?

6. Clara saw the smoke of a gun and heard the report 4 seconds afterward; how far was Clara from the gun?

7. Casper was 11,990 ft. distant from a quarry when he heard the report of a blast; how many seconds had elapsed since the explosion?

8. A boy standing opposite to a cliff heard the echo of his voice 6 seconds after having shouted; how far was he from the cliff?

9. If convenient, make some observations in sound and solve two problems similar to Exercise 5.

Oral.

REVIEW AND SUMMARY

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1. A garden in the form of a rectangle 30 yd. long and 40 yd. wide is to be represented on the blackboard. Name a convenient length to represent 1 yd.

2. What is the distance around the garden mentioned in Exercise I? What is the distance around the drawing?

3. How may lengths of 30 ft., 40 ft.; of 30 yd., 40 yd.; of 30 mi., 40 mi. be represented for the purpose of comparison? 4. What is the cost of 100 stamped envelopes at 264 a dozen?

5. If a postman has in his sack 200 pieces of mail averaging 2 oz. in weight, what is the weight of the mail?

6. What is the cost of 25 two-cent stamps, 2 dozen stamped envelopes, and 50 postal cards?

7. In 100 lb. of milk there are 4 lb. of fat; what part of the milk is fat?

8. A cow produces 400 lb. of milk in a month; according to Exercise 7, how many pounds of fat does she produce in this time? In 3 months at the same rate?

9. What is the cost of picking 5 tons of hops at 14 per pound?

10. How many bales of hops weigh 25 tons? What did it cost to dry these hops at $1 per bale?

II. A common kit of manual-training tools costs about $6; how much does it cost to supply 25 boys with these tools?

12. Read: 2,005; 20,005; 200,005. Name the places in each number beginning with units.

13. Instead of writing, state the figures beginning at tenthousands for seventy-five thousand, three hundred five.

14. In what way are figures grouped into periods in large numbers? Why are they so grouped? Name the periods in 376,542; in 300,000; in 2,300.

1. In $2.10 what figure shows the number of whole dollars? What figure shows the part of a dollar?

2. What name is given to the dot which separates the number of whole dollars from the part of a dollar?

3. How many tenths of a dollar are expressed by $.20 or by $.2?

4. Read as dollars and tenths of a dollar: $1.5; $2.5; $8.9; $125.5; $12.6; $.1;

$.4.

Similarly, a number of feet and tenths of a foot, or of pounds and tenths of a pound, or of anything else may be expressed by using the decimal point.

In reading a whole number and a number of tenths the decimal point is read "and." Thus, 1.2 ft. is read "One and two tenths feet."

The place at the right next to units' place is called tenths' place. The decimal point separates these two places.

Numbers expressed by use of the decimal point are said to be written decimally.

Write decimally :

9. Eleven and five-tenths.

II. Eighteen and one-tenth.

13. Express in cents: $2.4; $3.5; $11.1;

10. Seven and nine-tenths.

$.1;

12. Sixty and four-tenths. $.3; $.8; $.5; $.9;

$14.7.

1. If 40 yards of cloth are divided into ten equal parts, how many yards are there in one part? How many are there in seven of these parts?

2. Find

3. Find 6,520 oz.

of 40 yards. Find of 40 yards.

of 30 pounds; of 50 yd.; of 1,200 ft.; of

4. Find of $20; of $100; of 120 tons; of 970 days. 5. Write decimally:

6. Find .1 of 120 in.; of 70 weeks; of 400 mi. ; of 20 qt. 7. Find .7 of 90 days; of 120 minutes; of 140 ft.; of 70 tons.

8. How many tenths of a yard in two whole yards? In 3 yards? In 5 yd.? In 1 yd. and 5-tenths of a yard?

9. How many whole pounds are there in 30 tenths pounds? In 50 tenths pounds? In 20 tenths pounds?

10. Express in units and tenths: 17 tenths; 23 tenths; 81 tenths; 395 tenths.

II. Express decimally: 19 tenths; 29 tenths; 7 tenths; 175 tenths; 204 tenths.

12. Express in tenths: 2; 3; 5; 2.1; 2.3; 2.5; 23.4. 13. How many tenths of a dollar are ten times one-tenth of a dollar? How many dollars?

14. How many tenths of a dollar are ten times two-tenths of a dollar? How many dollars?

15. 10 times .1=?

16. 10 times 35 tenths =?

17. 10 times 405 tenths =?

10 times .2=?

10 times 3.5 =?

10 times 40.5=?

18. How many places is the decimal point moved to the right in multiplying by 10?

19. Multiply by 10 by moving the decimal point:

.3; .7; .9; 1.1; 1.9; 20.1; 29.8; 196.7; 2,879.3.