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10 ten-thousands are grouped into 1 hundred-thousand, and the number of hundred-thousands is written at the left next to ten-thousands' place.

1. In 762,804 what figure stands in units' place? In tens' place? In hundreds' place? In thousands' place? In ten-thousands' place? In hundred-thousands' place?

2. Write 325,689 and above each figure write the name of its place.

3. What does the position of each figure in a number tell? What does its value tell?

For convenience, the figures are separated by commas into sets of three each as far as possible, beginning at the right. These sets are called periods.

In reading, the word "thousands" is omitted in the case of ten-thousands and of hundred-thousands. The whole period is read as if it were units' period and then the word "thousand" is added. Thus, in the number 762,804, the second period is read: "Seven hundred sixty-two thousand."

This is similar to what is done in speaking of a number of people, or houses, or dollars. "Seven hundred sixty-two dollars," not "Seven hundred dollars, sixty dollars, two dollars."

We say,

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10. Add the numbers in each of the above columns.

II. Read: In 1900 the mines of the world produced:

80,643 tons of tin.

446,373 tons of zinc.

787,841 tons of lead.
543,735 tons of copper.

12. The capacity of the car-ferryboat Père Marquette is 30 cars; if the weight per car is 42 tons, how many hundred pounds does the boat carry when loaded?

13. Write twenty-five thousand, five hundred fifteen.

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1. Read the numbers in the table. The table shows the number of dollars earned by various railways during the third week of December for three consecutive years.

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2. Bring similar items cut or copied from newspapers

and read the numbers in class.

Write in figures:

3. Five hundred five thousand, seventy-five.

4. Five hundred thousand, seven hundred twenty-five. 5. Five hundred seventy-five thousand, seven hundred five. 6. Mount Everest is 29,002 ft. high and Pike's Peak is 14,147 ft. high. Find the difference in their heights.

7. At the mines 2,240 lb. of coal is regarded as a ton; how many pounds are there in a car-load of coal weighing 40 tons at the mines?

8. The State of Colorado has the form of a rectangle. It is 380 mi. long and 273 mi. wide; how many square miles are there in its area?

9. of the area of Colorado is covered by the Rocky Mountains; how many square miles is this?

10. The State of Wyoming has the form of a rectangle 254 mi. long and 249 mi. wide; how many square miles are there in its area?

II. What is the difference between the areas of Colorado and Wyoming?

12. There are 640 acres in a square mile; how many square miles are there in 128,000 acres?



1. Write the symbols that ordinarily appear on the clock-face.

2. For what numbers do these symbols stand?

3. What form is more common for four than IIII?

This way of writing numbers was used by the Romans, hence it is called Roman Notation. It is little used now, although it is still seen in the dates on title pages of books and in chapter headings. 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.

4. What is the Roman symbol for ten? For twelve?

5. The numbers from eleven to nineteen inclusive are written by placing the symbols for one, two, . . . nine at the right of the symbol for ten.

Write in Roman notation:

13, 15, 14, 19, 18, 17, 16.

6. Twenty is written as two tens, thus XX.

The num

bers from twenty-one to twenty-nine inclusive are written by placing the symbols for one, two, . . . nine at the right of XX. Thus, twenty-two is written XXII.

Write in Roman notation:

21, 25, 23, 26, 24, 29, 27, 28.

7. Thirty is written as three tens, thus XXX. The other numbers from thirty-one to thirty-nine are formed like those from twenty-one to twenty-nine.

Write in Roman notation:

31, 35, 34, 32, 36, 39, 38, 37.

8. Forty is written XL. L stands for fifty and X at the

left means ten less.


formed in the usual way.

other numbers to forty-nine are Write them.



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.




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 26¢ 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.

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