Introduction to decimal place values and the value of decimal digits. Created by Sal Khan and Monterey Institute for Technology and Education.
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.