Decimal place value

So I have a number written here. It's a 2, a 3, and a 5. And we already have some experience with numbers like this. We can think about 'what does it represent'. And to think about that we just have to look at the actual place values. So this right-most place right over here. This is the ones place. So this 5 represents five ones, or I guess you could say that's just going to be 5. This 3, this is in the tens place. This is the tens place, so we have three tens. So that's just going to be 30. And the 2 is in the hundreds place. So putting a 2 there means that we have two hundreds. So this number we can view as two hundred, thirty, five. Or you could view it as two hundred plus thirty plus five. Now what I want to do in this video is think about place values to the right of the ones place. And you might say 'wait, wait, I always thought that the ones place was the place furthest to the right.' Well everything that we've done so far, it has been. But to show that you can go even further to the right I'm going to put a little dot. I'm going to put a little dot right over here. We call that a 'decimal point'. And that dot means that anything to the right of this is going to be place values that are smaller, I guess you could say, than the ones place. So right to the left you have the ones place and the tens place and the hundreds place, and if you were to keep going you'd go to the thousands place and the ten thousands place. But then if you go to the right of the decimal point now you're going to divide by 10. So what am I talking about? Well, right to the right of the decimal point you are going to have-- find a new color-- this is going to be the tenths place. Well what does that mean? Well whatever number I write here that tells us how many tenths we're dealing with. So if I were to write the number 4 right over here, now my number is 2 hundreds plus 3 tens plus 5 ones plus 4 tenths. So you could view this a 4 times 1/10. Or you could write this as 4 tenths. Not tens, 4 tenths. Or 4 tenths is the same thing as this right over here. So this is a super important idea in mathematics. I can now use our place values to represent fractions. So this right over here, this 'point 4', this is 4/10. So another way to write this number-- I could write it this way, I could write it as two hundred, thirty-- let me do the thirty in blue-- two hundred and thirty five and four tenths. So I could write it like this, as a mixed number. So this up here would be a decimal representation: 235.4 And this right over here would be a mixed number representation: 235 and 4/10 but they all represent 200 plus 30 plus 5 plus 4/10. Let's look at a few more examples of this. So let's say I were to write the number 0.7-- and actually let me go one space even further to the right-- 0.76. So what would this be if I were to write it as a fraction? So let's just think about the place value. We have our decimal point. To the left of the decimal point is the ones place, but I have a zero there, so this is 0 ones. Now I have 7 tenths, so this is the tenths place. And then this is going to be this place to the right of that. We're going to divide by 10 again. So this is going to be the hundredths place. This space right over here is going to be the hundredths place. So this number right over here is-- we can rewrite it as 0-- let me write it this way-- we could rewrite it as 0 ones plus 7 tenths-- plus 7 tenths--- not tens, tenths-- plus 6 hundredths-- plus 6 hundredths-- not hundreds, hundredths. Or we could write this as 0 plus 7/10-- let me write that a little bit neater-- plus 7/10 plus 6/100-- 6 over 100. So you could write this-- 7/10 plus 6/100 is exactly what this is. You could say this is 0 ones, 7 tenths, and 6 hundredths. Now another way we could write this-- well look, if we wanted to write it as a fraction, or talk about it as a fraction-- I could ignore the 0, that's not going to change the value of the sum but I could add the 7/10 to the 6/100. So how could I write 7/10 in terms of hundredths? Well 7 over 10 is the same thing as 70 over 100. 7/10 is the same thing as 70 over 100. One way to thing about it is, if I multiply the denominator by 10 well, I can multiply the numerator by 10 as well and not change the value of it. 7/10 is the same thing as 70/100. And then you could add 6/100 to that-- 6/100 to that. And what will that give you? Well that's going to give you 76/100-- 76/100. So this number up here-- a lot of people will call this-- they might say 'zero point seven six' or they might call this 'seventy-six hundredths'. This is the hundredths place, this is the tenths place. But each tenth is worth ten hundredths. And you see that-- you could either view this as 7 tenths. or you could view it as 70 hundredths. So this is 76 hundredths. And you could keep going to the right. If you go to the right one more space you would get to the thousandths place and then the ten thousandths place. So you keep dividing by 10 each place you go to the right. And you multiply by 10 each place you go to the left.