means at his command, and to employ those means according to

his best judgment.

This book is intended to complete the course in arithmetic required by district and city schools.

M. A. BAILEY.

NOTATION AND NUMERATION

TERMS

A number answers the question, How

many?

Numeration is the process of reading numbers.

Notation is the process of writing num

bers.

ILLUSTRATION

How many apples? 6.

6, a number, or integer.

Read, Six.

Written, 6.

NUMERATION

In reading an integer, there are three steps:

The number is pointed off from right to left into periods of three figures each.

The periods are named from right to left to learn the name of the left-hand period.

The periods are read and named, but the period, 000, is not read and units' period is not named.

Pointing off into periods of three figures each

Beginning at the right, point off into periods:

7. How many figures may there be in the left-hand period?

8. How many figures must there be in each of the other periods?

Ex. 1. 3,600,028,371. Ex. 2. 23,600,028,371. Ex. 3. 423,600,028,371.

b.

- Naming the periods

1,023,438,019,000,320,678,735.

21,023,438,019,000,320,678,735.

c. 321,023,438,019,000,320,678,735.

From right to left, the periods are: units, thousands, millions, billions, trillions, quadrillions, quintillions, sextillions. ...; from left to right: .... sextillions, quintillions, quadrillions, trillions, billions, millions, thousands, units.

Higher periods after sextillions are: septillions, octillions, nonillions, decillions, undecillions, duodecillions,

....

9. Memorize the names of the periods from units to sextillions; from sextillions to units.

10. In a, beginning at the right, point to and name each period; then beginning at the left, point to and name each period.

11. In the same way, point to and name the periods in b and c. 12. In the same way, point to and name the periods in examples 1 to 6.

Ex. 10. Units, thousands, millions, billions, trillions, quadrillions, quintillions, sextillions; sextillions, quintillions, quadrillions, trillions, billions, millions, thousands, units.

Reading the periods

Each period is made up of three orders, units, tens, and hundreds. ILL. 368 equals 3 hundreds, 6 tens, 8 units.

In units' order, except when 1 is in tens' order, 1, 2, 3, 4, 5, 6, 7, 8, 9 are read one, two, three, four, five, six, seven, eight, nine.

In tens' order, 2, 3, 4, 5, 6, 7, 8, 9 are read twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety. 1 in tens' order is read with the units' figure. Thus: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19; ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen.

In hundreds' order, 1, 2, 3, 4, 5, 6, 7, 8, 9 are read one hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eight hundred, nine hundred.

O in any order is never read.