Return to the Purplemath home page

 

Try a MathHelp.com demo lesson Join MathHelp.com Login to MathHelp.com

 

Index of lessons | Purplemath's lessons in offline form |
Forums | Print this page (print-friendly version) | Find local tutors

 

Place Value: Whole Numbers (page 2 of 3)

Sections: Concepts, Whole-number place values, Decimal place values


Our fingers are called "digits", and so also are the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. ("Numerals" means "number characters".) We use these ten digits, along with the concept of place value, in exactly the same sense that we were using our fingers and our piles of marbles: a certain "place" tells us what unit we're working with, and the digit tells us how many we need of that unit.

So, for instance, the expression "264" means "two 100s, plus six 10s, plus four 1s", because hundreds, tens, and ones are what are stored in those particular places. In "expanded notation", "264" can be written as:

    200 + 60 + 4 = 2×100 + 6×10 + 4×1

Our place-value system is called the "decimal" system, because it's based on "all my fingers" being "ten fingers"; that is to say, the "base" of our number system is ten. We start with ones, being our fingers (that is, our counting "units"). Then we go to tens, being sets of fingers. Then we go to ten sets of sets of fingers, which is 10×10 = 100; that is, we go to hundreds. In other words, every time we go one "place" further to the left (that is, every time we go into a unit that is one times bigger than the previous place's unit), we multiply by our base of ten:

expression

 

place name

1  

 

  ones

10  

 

  tens

100  

 

  hundreds

1,000  

 

  thousands

10,000  

 

  ten thousands

100,000  

 

  hundred thousands

1,000,000  

 

  millions

10,000,000  

 

  ten millions

100,000,000  

 

  hundred millions

1,000,000,000  

 

  billions (or "milliard" in Europe)

1,000,000,000,000  

 

  trillions (or "billion" in Europe)

The commas marking off sets of three digits, like the comma between the 1 and the 0 in "1,000", are used to make it easier for people to read the numbers. Properly, if you spell out a number in words, you should use commas at those same spots. So "1,234" would be spelled out as "one thousand, two hundred thirty-four". Also, there should not be an "and" between the "hundred" and the "thirty-four"; you should not pronounce "234" as "two hundred 'and' thirty-four". Yes, I know that's how most people say it; it's still wrong. Copyright © Elizabeth Stapel 2013 All Rights Reserved

  • Write the number 32,067 in expanded notation.
  • To "expand" this number, I need to split it up into its different places. If I'm not sure of my places, I'll count them out, starting from the right-hand digit.

    This number has five digits. From the table above (if I haven't memorized this information yet), I know that this means that I'm dealing with tens of thousands. The one comma tells me that I'm dealing with thousands, too; one comma means I'm into the thousands, two commas would have meant I'm into the millions, and so forth.

    So I've got three 10,000s, two 1,000s, zero 100s, six 10s, and seven 1s. Usually, we ignore the zeroes in expanded notation, so this gives me:

      30,000 + 2,000 + 60 + 7

  • Write the standard form for the number which, in expanded notation, is written as follows:  9,000 + 300 + 2
  • I've got nine thousands, three hundreds, and two ones. I don't have any tens in the expanded form, so I'll need to use a zero in the tens place to keep that slot open. Then my standard form is:

      9,000 + 300 + 0 + 2 = 9,302

  • For the number 52,973, (a) state the place held by the 2, and (b) state the digit in the tens place.
  • a) The 2 is immediately to the left of the comma. I only have the one comma, so I know this number only goes into the thousands. In the thousands, I've got "52", so the 2 is in the thousands place. (The 5 is in the ten-thousands place.)

    b) The tens place is the second place, just to the left of the 3 in the ones place. There is a 7 in this second place, so the digit in the tens place is 7.

  • State the number 622,937,285 in words.
  • The commas break this number into digestible pieces. The "285" is in terms of ones, tens, and hundreds of ones (or of just "regular numbers", in extremely informal language). The "937" is in terms of ones, tens, and hundreds of thousands. And the "622" is in terms of ones, tens, and hundreds of millions.

millions

 

thousands

 

(regular)

622

 

937

 

285

    So the number they gave me, when I spell it out in words, is six hundred twenty-two million, nine hundred thirty-seven thousand, two hundred eighty-five.

<< Previous  Top  |  1 | 2 | 3  |  Return to Index  Next >>

Cite this article as:

Stapel, Elizabeth. "Place Value: Whole Numbers." Purplemath. Available from
    http://www.purplemath.com/modules/placeval2.htm. Accessed
 

 

 

MATHHELP LESSONS
This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2013-2014  Elizabeth Stapel   |   About   |   Terms of Use   |   Linking   |   Site Licensing

 

 Feedback   |   Error?