Decimal Place Value 127-4.0

This video is provided as supplementary
material for courses taught at Howard Community College and in this video I’m going to talk about
decimal place value. So let’s start out with place value for
whole numbers. We’ll do that as a review and
then go on to decimals. I’ve got the whole number 384. We know that the 3, the digit 3 in this
numbers is in what we call the hundreds column. So I’m gonna write a 100 over the 3. I could also write 100 as a
power of 10, I could write that as 10 squared. Now what this means is that the value of
3 in this number is going to be 3 times 100, or 3 times 10-squared. When I move over one column and I get to the digit 8, that 8 is inwhat we call the tens column,
so I’ll write a 10 above it. And if I want to express that 10 as a
power of 10, I can write 10 to the first. And this is going to mean that 8, that the value of the digit 8, in this number is 8 times 10. Moving over one more column, I get to
the 4. That’s in the units or the ones column. So I’ll write a one over the 4. To express the one as a power of 10, I can
just write that as 10 to the zero. And that means the value of th3 4 in
this number is going to be 4 times 1. Now let’s start adding decimal places. I’ll write a decimal point and a 7. So what’s the value of this 7? Well, if I look at my powers of 10,
I started out with 10-squared, and then 10 to the first and 10 to the zero,
so it looks like I’m ready for ten to the negative 1. Now 10 to the negative 1
is the same as 1 over 10, or one tenth, so this is the tenths column. and that 7 has a value of 7 times 1 over 10. When we read that we’re going to read
it as 384 and seven-tenths. Let’s add another number, another digit. Let’s add the digit 5 after that, and let’s see what its value would be. Well its column would be… we have a 10-squared column, and 10 to the first,
10 to the zero, and 10 to the negative 1… I’m ready for 10 to the negative 2. 10 to the negative 2 is the same as
1 over 10-squared, or 1 over 100, and this is going to be the hundredths
column. So the value of that 5 is 5 times 1 over 100. When we read this number, we’ll read the 384 and… and we’ll take the decimal part and just say 75 hundredths. We can add another decimal place.
Let’s add a 2. So that’s going to be in the
10 to the negative 3 column. 10 to the negative 3 is 1 over 1000, so that’s the thousandths column. So the 2 will have a value of 2 times 1 over 1000. At this point when we’re reading the number we can say 384 and 752 thousandths, or we might want to start saying things
like 384 point seven five two. As we add more and more
decimal places, it’s going to be more and more likely that we’ll just say point seven five two and then whatever
other decimal numbers we have, but basically this is the way that
decimal place value works. It’s just a continuation of the regular place value that
you already know. That’s about it, take care, I’ll see you next time.

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