Lesson 1 NUMERATION OF THE

One  1  Four  4  Seven  7  
Two  2  Five  5  Eight  8  
Three  3  Six  6  Nine  9 
Starting with Two, we say that each number is "one more" than the previous number. We say that we have "added one" to the previous number.
Thus Five is one more than Four. We have added one to Four to produce Five.
That is the first lesson in addition. It links the sequence of the names with their cardinality: how many.
So much for counting. Apart from that, each actual number is an autonomous whole. Your five fingers did not come about by adding one to four.
Tens. The name of the number one more than Nine is Ten: 10.
Ten is composed of ten Ones.
Its numeral is 1 followed by 0 (zero).
Let Ten now be the unit. On counting the Tens, here are their names and their numerals:
1 Ten  10  
2 Tens  are called Twenty  20  
3 Tens  are called Thirty  30  
4 Tens  are called Forty  40  
5 Tens  are called Fifty  50  
6 Tens  are called Sixty  60  
7 Tens  are called Seventy  70  
8 Tens  are called Eighty  80  
9 Tens  are called Ninety  90 
To form the numeral for each Ten, we followed each of the first nine numerals with a 0.
Numbers between two consecutive Tens. To compose the numbers between two consecutive Tens  between 30 and 40, for example  successively add the first nine numbers to the lower Ten. To write their numerals, successively replace the 0 of the lower Ten with the first nine numbers.
Here are the numbers between 30 and 40:
31  Thirtyone  (Which means: "One more than Thirty.")  
32  Thirtytwo  
33  Thirtythree  
34  Thirtyfour  
And so on. 
The numbers between 10 and 20, however, have unique names:
11  Eleven  
12  Twelve  
13  Thirteen  
14  Fourteen  
15  Fifteen  
And so on. 
We have now named the numbers 1 through 99, and constructed their numerals.
Hundreds. A collection of ten Tens form the number One Hundred. Its numeral is 100. Upon letting One Hundred be the unit, we count those Hundreds and name them as follows:
1 Hundred  100  
2 Hundreds  are called Two Hundred  200  
3 Hundreds  are called Three Hundred  300  
4 Hundreds  are called Four Hundred  400  
And so on. 
Numbers between two consecutive Hundreds. To compose the numbers between two consecutive Hundreds  between 300 and 400, for example  successively add the first ninetynine numbers to the lower Hundred. To write their numerals, successively replace the two 0's of the lower Hundred with the numerals of the first ninetynine numbers.
For example: Three Hundred One (301), Three Hundred Two (302), Three Hundred Three (303), . . . , Three Hundred Ninetyeight (398), Three Hundred Ninetynine (399).
In this way we name the numbers 100 through 999, and construct their numerals.
We have now then constructed the names and the numerals for all the numbers 1 through 999. In the next Lesson, we will see that to name any whole number, however large, it is sufficient to know the names through 999.
Also in the next Lesson we will analyze our system of numeration in terms of place value. And in Lesson 3, we will extend our system to decimals.
The student should begin mastering Elementary Addition and the Multiplication Table.
At this point, please "turn" the page and do some Problems.
or
Continue on to the next Lesson: The Powers of 10
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Copyright © 2017 Lawrence Spector
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