Decimal place value

what is the place value of 3 in 654 point 2 1 3 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 2 2 1 want to make sure I have enough colors here 2 1 3 now we're pretty familiar I think with what goes on to the left of the decimal point we know that this right here reduce in a neutral color that this right here is the hundreds this is the hundreds place or we could view that as 10 to the 2nd 10 to the 2nd let me write that a little bit bigger down here so this right here is the hundreds that is the hundreds place or you could view that as the 10 to the 2nd place which is the same thing as 100 this right here is the tens place which is the same thing as 10 to the 1st this right here is the ones place which is the same thing as 10 to the 0 then if you go to the right of the decimal point one place to the right of the decimal point this represents tenths this represents tenths or we could view it as I could write it like this this represents tenths or 10 to the negative one then if we go to this magenta if we go to places to the right this represents hundredths this represents hundredths or 10 to the negative 2 and then finally this 3 this represents thousandths this represents thousands or 10 to the negative 3 now just to answer the question what is the place value of 3 in 654 point 2 1 3 the place value is thousandths the place value is thousands and we'd 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 right we have six hundreds plus five tens or you could say plus 50 plus 50 plus four ones so plus four ones plus like the four is net other color plus four ones plus two tenths so plus two tenths plus one hundredths plus one hundredths plus three thousandths plus three over one two three thousandths 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 six times 100 plus five times 10 plus four times one I keep doing that in the wrong color plus four times 1/4 times one plus two times 1/10 plus 2 2 times 1/10 plus plus 1 times 1 over 100 and then finally plus 3 times 1 over 1,000 so hopefully this when you write it out like this gives you a sense of what it means when we say place value the six to one to three digits to the left of the decimal is in the hundreds place so it represents six hundreds this represents five tens because it's in the tens place this represents four ones you go to the thousands place this three literally represents three one thousandths