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). Hope this helps. Please ask more questions if it doesn't. Sincerely, - Doctor Ameis, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.