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Place Value: Concepts (page 1 of 3)

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


To explain the concept of "place value", I'll start with some comparisons. First, let's look at the word "records" in these two sentences:

  • Security camera 4 records all activity in the rear of the building.
  • The security office stores the records from every shoplifter they've caught in the last five years.

In the first sentence, "records" is pronounced as "reh-KORDZ" and is a verb; in the second sentence, "records" is pronounced as "REH-kerdz" and is a noun. The "value" of the word changed, depending on the word's "place" in the sentence structure.

Now, let's imagine looking at the security footage being stored in the security office; in particular, we'll look at the 24-hour timestamps 00:00:15, 00:15:00, and 15:00:00. (The 24-hour timestamps mean, for instance, that "1 PM" is "13 hours". The first timestamp, 00:00:15, means "zero hours, zero minutes, and fifteen seconds"; in other words, fifteen seconds after midnight. The second timestamp, 00:15:00, means "zero hours, fifteen minutes, and zero seconds"; in other words, exactly fifteen minutes past midnight. The third timestamp, 15:00:00, means "fifteen hours, zero minutes, and zero seconds"; in other words, exactly three o'clock in the afternoon. In each of these timestamps, the "15" told the time. But the "15" meant a different thing in each case — 15 seconds, 15 minutes, or 15 hours, depending on the context — and the "place" where the "15" was told us what the "value" of the "15" was for that particular timestamp.

Note also how important the zeroes were. Without the zeroes, "00:00:15" would have collapsed into just "15". Those zeroes held the "hours" and "minutes" slots in place, preserving the meaning of the timestamp. Since the value of "15" varies with the place, it is vitally important that those other places not disappear. Copyright © Elizabeth Stapel 2013 All Rights Reserved


Let's think about counting. When we were little kids, we started counting on our fingers. If we were counting up ("tallying") a larger number of things, we might write down tally marks to keep track:

tally marks

But once we got into bigger numbers, the thicket of tally marks started being unhelpful.

lots of tally marks

We could count up to ten on our fingers, but what then? We were out of fingers. But let's say we had some marbles. Every time we used up all of our fingers, we could go back to fists (zero fingers) and we could put a marble down, standing for "one time of all-my-fingers" (that is, once of ten).

one marble (one 10) and no fingers (no 1s)

So three marbles and two fingers would be "three times of ten, plus another two", or "thirty-two":

three marbles (three 10s) and two fingers (two 1s)

When we get ten marbles in the pile, we can't count any more of "all-my-fingers" because we're out of fingers to use for counting the marbles. So let's start a second pile, further away, to stand for "ten 'all-my-fingers' marbles". We'll call "ten 'all-my-fingers' marbles" (that is, ten times of ten) a "one hundred". Then this:

two marbles (two 100s), then another six marbles (six 10s), and finally four fingers (four 1s)

...means "two times of ten-times-of-ten, plus six times of all-my-fingers, plus another four fingers", or "two hundred sixty four".

Of course, if somebody trips over our piles of marbles, we'll lose count. Once the marbles are no longer in their proper places, we can't tell what values they're meant to represent. In written numbers, this "the value depends on where the marble was" is the point of "place values" in writing number names.

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Cite this article as:

Stapel, Elizabeth. "Place Value: Concepts." Purplemath. Available from
    http://www.purplemath.com/modules/placeval.htm. Accessed
 

 

 

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