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What is the place value of 3 in 654.213?

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So let's think about that a little bit.

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And to do that, let me rewrite the number, and I'll write

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each digit in a different color.

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So we have 654 point-- we get the decimal point-- 213.

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Now we're pretty familiar, I think, with what goes on to

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the left of the decimal point.

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We know that this right here-- let me do this in a neutral

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color-- is the hundreds place, or we could view that as 10 to

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the second.

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Let me write that a little bit bigger down here.

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So this right here that is the hundreds place, or you could

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view that as the 10 to the second's place, which is the

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same thing as hundred.

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This right here is the tens place, which is the same thing

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as 10 to the first. This right here is the ones place, which

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is the same thing as 10 to the zero.

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Then if you go one place to the right of the decimal

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point, this represents tenths.

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This represents tenths, or we could view it as 10 to the

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negative one.

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Then, if we go to this magenta, if we go two places

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to the right, this represents hundredths, or 10 to the

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negative two.

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And then finally, this 3 represents thousandths.

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This represents thousandths, or 10 to the negative three.

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Now, just to answer the question what is the place

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value of 3 in 654.213?

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The place value is thousandths.

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That would essentially answer their question.

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But to make sure that we really understand what this

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means, I'm going to rewrite this number.

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We can rewrite this number as 600.

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We have 6 hundreds plus 5 tens, or you could say plus 50

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plus 4 ones plus 2/10, plus 1/100, plus 3/1,000.

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Or we could write this, just to really make sure we

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understand what we're talking about when we mean place

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value, we can rewrite this number as 6 times 100, plus 5

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times 10, plus 4 times 1-- I keep doing that in the wrong

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color-- plus 2 times 1/10, plus 1 times 1/100, and then

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finally, plus 3 times 1/1,000.

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So hopefully, when you write it out like this, it gives you

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a sense of what it means we say place value.

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The 6, three digits to the left of the decimal, is in the

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hundreds place, so it represents 6 hundreds.

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This represents 5 tens because it's in the tens place.

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This represents 4 ones.

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You go to the thousandths place, this 3 literally

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represents three one-thousandths.

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