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# Decimal place value

Video transcript

What is the place value
of 3 in 654.213? So let's think about
that a little bit. And to do that, let me rewrite
the number, and I'll write each digit in a different
color. So we have 654 point-- we get
the decimal point-- 213. Now we're pretty familiar, I
think, with what goes on to the left of the decimal point. We know that this right here--
let me do this in a neutral color-- is the hundreds place,
or we could view that as 10 to the second. Let me write that a little
bit bigger down here. So this right here that is the
hundreds place, or you could view that as the 10 to the
second's place, which is the same thing as hundred. This right here is the tens
place, which is the same thing as 10 to the first. This right
here is the ones place, which is the same thing as
10 to the zero. Then if you go one place to
the right of the decimal point, this represents tenths. This represents tenths, or we
could view it as 10 to the negative one. Then, if we go to this magenta,
if we go two places to the right, this represents
hundredths, or 10 to the negative two. And then finally, this 3
represents thousandths. This represents thousandths, or
10 to the negative three. Now, just to answer the question
what is the place value of 3 in 654.213? The place value is
thousandths. That would essentially answer
their question. But to make sure that we really
understand what this means, I'm going to rewrite
this number. We can rewrite this
number as 600. We have 6 hundreds plus 5 tens,
or you could say plus 50 plus 4 ones plus 2/10, plus
1/100, plus 3/1,000. Or we could write this, just
to really make sure we understand what we're talking
about when we mean place value, we can rewrite this
number as 6 times 100, plus 5 times 10, plus 4 times 1-- I
keep doing that in the wrong color-- plus 2 times 1/10, plus
1 times 1/100, and then finally, plus 3 times 1/1,000. So hopefully, when you write it
out like this, it gives you a sense of what it means
we say place value. The 6, three digits to the left
of the decimal, is in the hundreds place, so it represents
6 hundreds. This represents 5 tens because
it's in the tens place. This represents 4 ones. You go to the thousandths
place, this 3 literally represents three
one-thousandths.