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Tredecillions.

Duodecillions.

Undecillions.

Decillions.

Nonillions.

Octillions.

Septillions.

Sextillions.

Reference Table.

=

275,301,246,157,896,275,832,456,297,143,215,367,291,326,415.

NOTE 1.-The names of the periods above tredecillions are: quatuordecillion, quindecillion, sexdecillion, septendecillion, octodecillion, novemdecillion, and vigintillion.

Quintillions.

Quadrillions.

Trillions.

Billions.

Millions.

Thousands.

16. Note the number of decimal places in each of the following expressions:

=

1. .44 tenths. (1 decimal place.)

2. .27=27 hundredths. (2 decimal places.)
3. .346 346 thousandths. (3 decimal places.)
4. .2758 2758 ten-thousandths.

5. .072867286 hundred-thousandths.

6. .000896 896 millionths. (6 decimal places.)
7. .000,468,275= billionths. (9 decimal places.)

8. .000,000,000,462 =
=

trillionths.

9. .000,000,000,000,527

=

10. .000,000,000,000,000,004
11. .000,000,000,000,000,000,037
12. .000,000,000,000,000,346,275 =
13. .000,000,000,000,002,427,836 =

14. In any number of thousandths there are

mal places.

15. In any number of millionths there are places.

16. In any places.

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Primary units.

quadrillionths.

— quintillionths.

number of billionths there are

deci

decimal

decimal

Algebra - Notation.

17. Letters are used to represent numbers; thus, the letter a, b, or c may represent a number to which any value may be given.

18. Known numbers, or those that may be known without solving a problem, when not expressed by figures, are usually represented by the first letters of the alphabet; as, a, b, c, d.

ILLUSTRATIONS.

(a) To find the perimeter of a square when its side is given.
Let a one side.*
Then 4 a

=

the perimeter.

Hence the rule: To find the perimeter of a square, multiply the number denoting the length of its side by 4.

(b) To find the perimeter of an oblong when its length and breadth are given.

Let a = the length.

Let the breadth.

=

Then 2a + 2b, or (a + b) × 2 = the perimeter.

Hence the rule: To find the perimeter of an oblong, multiply the sum of the numbers denoting its length and breadth by 2.

(a) There are two three times the first.

Let
Then

and

19. Unknown numbers, or those which are to be found by the solution of a problem, are usually represented by the last letters of the alphabet; as, x, y, z.

ILLUSTRATION.

numbers whose sum is 48, and the second is What are the numbers ?

x= the first number. 3x the second number x+3x=48.

4x=48.

x = 12.

3 x = 36.

The numbers are 12 and 36.

* That is, the number of units in one side. The letter stands for the number.

Reference Table.

Boudoul

275,301,246,157,896,275,832,456,297,143,215,367,291,326,415.

Tredecillions.

NOTE 1.- The names of the periods above tredecillions are: quatuordecillion, quindecillion, sexdecillion, septendecillion, octodecillion, novem decillion, and vigintillion.

16. Note the number of decimal places in each of the following expressions :

=

1. .44 tenths. (1 decimal place.)

2. .2727 hundredths. (2 decimal places.)

3. .346 346 thousandths. (3 decimal places.)

4. .2758 2758 ten-thousandths.

=

5. .072867286 hundred-thousandths.

6. .000896 896 millionths. (6 decimal places.)
7. .000,468,275 = billionths. (9 decimal places.)

trillionths.

8. .000,000,000,462 = 9. .000,000,000,000,527 10. .000,000,000,000,000,00411. .000,000,000,000,000,000,037 12. .000,000,000,000,000,346,275 13. .000,000,000,000,002,427,836 = 14. In any number of thousandths there are mal places.

=

15. In any number of millionths there are places.

16. In any number of billionths there are places.

=

-=

=

quadrillionths.
quintillionths.

==

=

deci

decimal

decimal

Algebra - Notation.

17. Letters are used to represent numbers; thus, the letter a, b, or c may represent a number to which any value may be given.

18. Known numbers, or those that may be known without solving a problem, when not expressed by figures, are usually represented by the first letters of the alphabet; as, a, b, c, d.

ILLUSTRATIONS.

(a) To find the perimeter of a square when its side is given.
one side.*

Let a
Then 4 a

the perimeter.

=

Hence the rule: To find the perimeter of a square, multiply the number denoting the length of its side by 4.

(b) To find the perimeter of an oblong when its length and breadth are given.

Let a = the length.

Let b = the breadth.

Then 2a+2b, or (a + b) × 2 = the perimeter.

(a) There are two three times the first.

Let
Then

and

Hence the rule: To find the perimeter of an oblong, multiply the sum of the numbers denoting its length and breadth by 2.

=

19. Unknown numbers, or those which are to be found by the solution of a problem, are usually represented by the last letters of the alphabet; as, x, y, z.

4x=48.

= 12.

ILLUSTRATION.

numbers whose sum is 48, and the second is What are the numbers? - the first number. 3x the second number x+3x=48.

x=

x=

3 x = 36.

The numbers are 12 and 36.

* That is, the number of units in one side. The letter stands for the number.

20. The sign of the multiplication is usually omitted between two letters representing numbers, and between figures and letters; thus, a x b, is usually written ab; b x 4, is written 4 b. 6 ab, means, 6 times a times b, or 6 × a × b.

21. EXERCISE.

Find the numerical value of each of the following expressions, if a = 8, b = 5, and c = 2:

1. a+b+c=

2. a + b

5. 2 ab=

=

6. 3 abc

7. 2ab+5c=

8. ab+bc=

(a) Find the sum of the eight results.

c =

3. 2a+b+c=

4. a+b-2c=

1. 3(a+b)=*

2. 2(a - b)=

3. 4 (a+b+c)=

4. 2(a+b−c)=

22. EXERCISE.

Find the numerical value of each of the following expressions, if a = 20, b = 4, and c = 2:

=

=

5. a÷b=

6. (a+b)÷c=†

7. (a+b)+3c=

8. (a+2b)÷2c=

23. EXERCISE.

2. If 5x = 40,
x = ?

(b) Find the sum of the eight results.

1. If 2x=20,

x = ?

4. If 2x+3x=60,
x = ?

*This means, 3 times the sum of a and b.
This means, the sum of a and b, divided by c.

3. If 6x=72,

x = ?

5. If 3x+4x=56,

x = ?

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