Saturday, October 12, 2013

Number System: Dicimal Number: Place value

Place Value

Our Number System is based on ten.
Using only ten symbols (called Digits) we can write any number.

The Ten Digits

The Digits we use today are called "Hindu-Arabic Numerals" and look like these:
0   1   2   3   4   5   6   7   8   9

You can use these on their own to count up to 9.

Ten Or More ...

When we have more than 9 items, we start another column - the "tens" column - and we write down how many "tens" we have, followed by how many ones (called "units"):
1 2
ten balls one ball one ball
The Number "12"

So we know that we have 1 Ten and 2 Ones, which makes 12.
This could also be written as 1 × 10 + 2 × 1.
Example: "35" means 3 Tens and 5 Units, which is also 3 × 10 + 5 × 1

A Hundred Or More ...

When we have more than 99 items, we start another column - the "hundreds" column. Now we need to show how many hundreds, tens and units:
1 4 3
ten balls ten balls ten balls ten balls ten balls one ball one ball one ball
The Number 143

So we know that we have 1 Hundred, 4 Tens and 3 Ones
This could also be written as 1 × 100 + 4 × 10 + 3 × 1.
Example: "369" means 3 Hundreds, 6 Tens and 9 Units, which is also 3×100 + 6×10 + 9×1

And So On ...

So, each time we need to show a bigger number we just add one column to the left and we know it is always 10 times bigger than than the column on its right.
each new column on the left is ten times bigger
So, where we PLACE a digit is important!


What if we have 1 Ten, but no Units? We show that we have no units by using a zero there:
1 0
ten balls
The Number "10"
We have to put a zero, or "10" would look like "1".
We use the same thing to show zero tens, hundreds, etc
Example: "203" means 2 Hundreds, Zero Tens and 3 Units.

Names for Each Column

These are the names of each column:
Millions Hundred-Thousands
(For bigger amounts, see Metric Numbers)


In a place-value table write down the number eleven thousand, three hundred and twenty seven:
1 1 3 2 7
The Number 11,327

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