Sam's Blog: How to Understand the Concept of Zero ( 0 )

How to Understand the Concept of Zero ( 0 ): "

We are usually taught to count 'one to ten' first. Then, we are told that zero is a placeholder. After that we learn that it is equal to nothing. In this article, you'll learn a much easier way to understand the concept of zero.

Steps

Count from zero ( 0 ) to nine ( 9 ). Believe it or not, that is ten numbers.
Write down the numbers zero ( 0 ) through nine ( 9 ). Then write how many numbers you have counted directly below:

0 1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9 10
- When presented like this, you can plainly see that you need two digits because all have been used already. Yet, you still may be confused.
Understand that any number of zeros may correctly be in front of a number.
Repeat the writing exercise, except add a leading zero to the first line and continue with tens on the next.

00 01 02 03 04 05 06 07 08 09

10 11 12 13 14 15 16 17 18 19
- Compare this with the confusing way you were probably taught in school:
  
  1 2 3 4 5 6 7 8 9 10
  
  11 12 13 14 15 16 17 18 19 20
- Note (in the second example) that the last number always has a change in the tens digit.
Understand that each position indicates ten of the previous group; the digit in that position indicates the number of groupings of ten of that group.
- The English language has made this more confusing than it actually is. For example, 10, 20, 30, through to 90 would be better taught as 1 ten, 2 tens, 3 tens, etc., instead of 'ten, twenty, thirty, forty, etc.' All of the tens grouping numbers starting with 20 are contractions of 'Two tens, three tens, four tens, etc.', except that you do not use an apostrophe. Children could be taught the contractions later.
- If you have a problem with using '1 ten', consider this; after 99, we say 'one hundred' though we often just say 'hundred' or 'a hundred'. This is no different from when we simply say 'ten'.
Continue writing numbers with leading zeros until you reach 99:
00 01 02 03 04 05 06 07 08 09
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
- This is a good time to imagine the leading zeros that could be in front of all these numbers.
- Note the continuity of the pattern of numbers. Placing a '1' in the hundreds column and changing the tens and units columns to zero is only natural.
- Another activity you could do is this:
  Make ten copies of the listing of numbers from 00 to 99.
  Place big (as tall as the group) leading numbers, starting with zero, in front of each group.
  This is a quick way to illustrate counting to 999 without writing down every number.
  - This could also have been done with the smaller tens group, but the effect is less profound.
Reflect. You should now be able to reach the conclusion that zero ( 0 ) represents a nil value for the numeric grouping (units, tens, hundreds, etc) that it represents. Zero is no longer just a 'Placeholder' but a representation of value.