EXERCISES IN READING AND WRITING NUMBERS.

Read the foregoing numbers, consulting the headings, till you get accustomed to the names of the periods.

Read also as follows, or as may be directed by the teacher.

a. Read the tens' and ones' columns in the first period on the right.

b. Read all the numbers of the ones' period.

c. Read the right-hand column in the thousands' period.

d. Read the tens' and ones' columns in the thousands' period. e. Read the two right-hand periods.

f. Read the right-hand column of the millions' period with the left of thousands, as hundred thousands.

g. Read the millions' and ones' periods, omitting the thousands' period as if filled with ciphers.

Note. These exercises may be varied to almost any extent.

3. Write and read 2,000,000; 5,000,000; 7,000,000; 4,000,000. Fill the places occupied by ciphers with any digits you choose, and then read the numbers thus formed. Do this in various ways.

4. Copy the following numbers, and read them; then erase the digit at the right hand, and arrange the periods anew, by placing the commas where they should be, and read:

1,635,987 416,429,863 134,764,211 7,763,664 29,876,354 Continue this exercise by erasing the digits one by one, and pointing off the periods correctly.

5. How many tens, hundreds, thousands, ten-thousands, hundred-thousands and millions are expressed in those places respectively, in the numbers of Exercise 4 ?

Review Exercises.

Hundreds.-1. Write 300 and 20 and 7 as one number, expressed by three figures. In the same way write:

Thousands.-4. Make the following numbers larger by one thousand 328, 456, 508. By three thousand. By five thousand. 5. What number is next greater than 1599, 3019, 4091, 8400, 6379, 4599, 9999, 8765, 9109, 3099, 4098?

6. What number comes next before 2000, 7000, 4600, 5060, 3010, 2790, 8970, 1000, 1010, 7801 ?

7. Count and write from 996 to 1006; from 3189 to 3200; from 7990 to 8012; from 3001 back to 2989; etc.

8. How many hundreds and tens in 43 tens? In 68, 37, 56, 27, 49, 168, 434 tens? How many in 386 units? In 468, 125, 632 units? In 354, 538, 624 tens?

9. How many thousands and hundreds are in 25 hundreds ? In 61, 52, 47, 56 hundreds? How many in 250 tens? In 310, 161, 289, 364, 543 tens? How many in 6987 units?

Tens and Hundreds of Thousands.-10. Prefix first twenty, then sixty, then forty thousand to 438, 132, 596, 100.

11. What number next greater than 25,999 ? 130,109 ? 199,999? 888,889? 986,290? 18,400? 689,999 ?

12. What number next less than 300,001 ? 700,000? 147,000? 354,989? 500,790 ? 100,000? 600,999? 489,123? 500,000 ?

Definitions.

12. A unit is one of any order or kind.

13. A number is a unit or collection of units.

14. Notation is the expression of number by figures or letters. 15. Numeration is the reading of numbers written in letters or figures.

16. All the digits have a Simple Value and a Local Value. A simple value, when they represent units or ones; a local value, when used to express tens, hundreds, etc. This value is called local because it depends on the place which the digit occupies (its locality).

17. The nine digits are signs of number, hence they are called Significant Figures. In this sense, the cipher "0" is not a significant figure.

Roman Notation.

18. The following table gives a complete view of a method of representing numbers by letters. This is called the Roman method because first used by the Roman people.

Note 1. It will be noticed that in writing four and nine of each order, a letter of less value is placed before one of greater value. In this case the less value is deducted from the greater. Thus, XL (ten less than fifty) is written for XXXX. CD (one hundred less than five hundred) is written for CCCC, etc. This mode of abbreviation is common, not universal.

Note 2.-A bar over a letter, or combination of letters, increases its value a thousand times.

For writing numbers in Roman numerals, we have the following 19. Rule.-Write the several terms in order as given in the table.

EXERCISES IN THE ROMAN NOTATION.

1. Read XXIV, IX, XIX, XV, XIV, LX, XLIV, LXXXIX, XC, XCIX, CCI, CCCXCIX, CD, CDLVIII, CDLIX.

2. DV, CDXCIX, DXLVI, DCCCIX, CMXCIX, MD, MIX, LIX, DIX, MDCCCLXXXIV, MCDLXX.

3. Write in Roman numerals, 54, 72, 83, 59, 119, 72, 38, 49, 63, 98, 75, 69, 43, 91, 108, 319, 444, 333, 991, 3847, 2563, 3482.

Examples.-1. A hunter shot 6 rabbits on Monday, 7 on Tuesday, 8 on Wednesday, but only one on Thursday. How many rabbits did he shoot?

2. Charles is 9 years old. How old will he be in 6 years? In 5 years? In 8 years?

3. Fred had 8 dollars in his bank; he received 7 more on his birthday, and 4 at Christmas. How much had he then ?

4. Grandfather was 53 years old when his grandchild was born. How old is he now that his grandchild is 9 years old?

5. The sun rose at 6 o'clock this morning; that was 3 hours ago. What o'clock is it now? What o'clock 5 hours after sunrise? 4 hours? 6 hours?

6. William read 7 pages in the morning, 3 in the afternoon, and 4 in the evening. How many pages did he read that day?

7. Sarah goes up and down stairs 8 times in the morning, and 5 times in the afternoon. How many times in the day?

8. Count to one hundred.-Count by twos to 100.-Count by threes to 99. Count by fours to 100.-Count by fives to 100.Count by sixes to 96.-Count by sevens to 98.-Count by eights to 96.-Count by nines to 99.

The pupil may first write the result of each successive addition, and afterward go through the exercise orally.

9. How many units in 10 twos? (Count by 2's till you find out.) How many in 10 threes? In 10 fours? In 10 fives? etc.