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### Expanded and Standard Forms

```
Date: 09/06/98 at 22:11:41
From: Mark Leblanc
Subject: Expanded form/standard form

My teacher has asked me to write numbers in standard form and expanded
form. For example 4,017. What exactly does she want me to do?

Thank you for taking the time to read this letter.

Mark
```

```
Date: 09/15/98 at 15:46:04
From: Doctor Ameis
Subject: Re: Expanded form/standard form

Hello Mark,

Expanded form is a way of writing numbers so that all that is hidden
about them comes out into the open.

The simplest way to write numbers in expanded form is to write them
sort of in English.

For 4,017, this becomes 4 thousands and 0 hundreds and 1 ten and 7
ones. This can be made to look like math by changing the words to math
symbols.The expanded form for 4,017, then, is:

4 x 1000 + 0 x 100 + 1 x 10 + 7 x 1

The expanded form shows what each digit is worth (for example, the 4
is worth 4 x 1000, which is the same as 4 thousands, which equals
4000).

Here is another example.

12,345 becomes 1 ten thousand and 2 thousands and 3 hundreds and 4 tens
and 5 ones. Changing the words to math symbols, 12,345 in expanded form
is:

1 x 10,000 + 2 x 1,000 + 3 x 100 + 4 x 10 + 5 x 1

Standard form is the reverse of expanded form. You begin with expanded
form and change it to the way we normally write numbers.

For example, 3 x 1,000 + 5 x 100 + 7 x 10 + 4 x 1 can be changed to
3 thousands and 5 hundreds and 7 tens and 4 ones. This becomes:

3000 + 500 + 70 + 4

Do the addition and you get 3574 (the standard form).

Sincerely,

- Doctor Ameis, The Math Forum
http://mathforum.org/dr.math/
```
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