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Identify Value

Nosotros write numbers using only ten symbols (called Digits).
Where nosotros place them is important.

The Ten Digits

The Digits we use today are chosen "Hindu-Arabic Numerals":

0   1   two   3   four   5   6   7   8   9


We can use these on their own to count upwardly to 9:

0
i one ball
2 one ball one ball
three one ball one ball one ball
four one ball one ball one ball one ball
5 one ball one ball one ball one ball one ball
6 one ball one ball one ball one ball one ball one ball
vii one ball one ball one ball one ball one ball one ball one ball
eight one ball one ball one ball one ball one ball one ball one ball one ball
ix one ball one ball one ball one ball one ball one ball one ball one ball one ball
?? one ball one ball one ball one ball one ball one ball one ball one ball one ball one ball

But what happens later on 9?

10 Or More ...

When we have more than than nine items, we start some other column - the "tens" column - and we write downwardly how many "tens" nosotros accept, followed past how many "ones" (likewise called "units").

And then we write:

Example: this is how we write downwardly twelve:

The Number "12"

place value 12 tens ones is 10 2

It says we accept ane Ten and ii Ones, which makes 12.

This can also be written as 1 × 10 + 2 × 1.

Example: "35" means three Tens and 5 Ones, which is also 3 × ten + 5 × 1

The Number "35"

Zero

What if we have one 10, merely no Ones? We show "no Ones" by putting a zero in that location:

Tens

Ones
1 0
ten balls

The Number "10"

We accept to put a Zero in the Ones place or "10" looks similar "i".

place value 10

A Hundred Or More ...

When we have more than than 99 items, we start another column - the "hundreds" column. At present we need to show how many Hundreds, Tens and Ones:

The Number 143

That shows nosotros have i Hundred, 4 Tens and 3 Ones:

This can as well be written as 1 × 100 + 4 × 10 + three × 1.

place value 369: 300 60 9

Example: "369" means 3 Hundreds, six Tens and 9 Ones

Which is also 3 × 100 + 6 × 10 + ix × 1

We likewise use a Null when there are no Tens:

Case: "104" means 1 Hundred, Zilch Tens and 4 Ones.

The Number 104

And So On ...

Each time nosotros desire to show a bigger number we merely add one column to the left and nosotros know information technology is always x times bigger than than the column on its correct.

each new column on the left is 10 times bigger

And then, where nosotros Identify a digit is important!

Names for Each Column

These are the names of each cavalcade:

Millions Hundred-Thousands

Ten-Thousands

Thousands

Hundreds

Tens

Ones

(For bigger amounts, see Metric Numbers)

Example: The number 11 1000, iii hundred and twenty seven in a place value table:

Ten-Thousands

Thousands

Hundreds

Tens

Ones
ane ane three 2 7

The Number 11,327

1686, 1687, 1688, 1689, 1690, 1691, 5875, 5876, 5877, 5878