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Current time:0:00Total duration:6:26
CCSS.Math:

Video transcript

so I have a number written here it's a two a three and a five 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 rightmost place right over here this is the ones place so this five represents five ones or I guess you could say that's just going to be five this three this is in the tens place this is in the tens place so we have three tens so that's just going to be 30 and the to the two is in the hundreds place so putting a two 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 then 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 in the ten thousands place but then if you go to the right of the decimal point now you're going to divide by ten 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 this is going to be the tenths place well what does that mean well if whatever number I write here that that tells us how many tenths we're dealing with so if I were to write the number if I were to write the number four right over here now my number is two hundreds plus 3 tens plus five ones plus four tenths so I you could view this as 4 times 1/10 or you could write this as four tenths not tens for ten or 4/10 is the same thing as 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 for this is 4/10 so another way to write this number I could write it this way I can write it as 200 230 let me do the 30 in blue 230 235 and 4/10 so I could write it like this as a mixed number so this up here would be a decimal representation 235 point 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 tens let's look at a few more examples of this so let's say I were to write the number let's say I were to write the number zero zero point seven and actually let me go one space even further to the right zero point seven six 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 zero ones now I have seven tenths so this is the tenths place and then this is going to be this place to the right of that that's going to be that's going to be that's going to we're going to divide by 10 again so this is going to be the hundredths place so let me write this now this base right over here is going to be the hundredths 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 1 0 1 s plus 7 tenths plus 7/10 not tens tenths plus six hundredths plus six hundredths not hundreds hundreds or we could write this as 0 plus plus 7/10 write that a little bit neater plus 7 tenths plus 6 hundredths plus 6 hundredths 6 over 100 so you can write this 7 tenths plus 6 over 6 hundredths is exactly what this is you could say this is zero ones seven tenths and six hundredths now another way we could write this you might be tempted well look if we wanted to write it as a fraction or talk about it as a fraction I can ignore the zero that's not going to change the value of this sum but I could add the 7/10 to the six hundredths so how can I write 7/10 in terms of hundredths well 7 over 10 is the same thing as 70 over a hundred is the seven tenths is the same thing as 70 over 100 one way to think about it is if I have 10 tie if I multiply the denominator by 10 well I can multiply the numerator by 10 as well and not change the value of it seven tens the same thing as 70 hundredths and then you could add 600 600 stood at and what will that give you well that's going to give you seventy six hundredths seventy six hundredths so this number up here a lot of people will call this you they might say 0.76 or they might call this 76 hundredths 76 hundredths this is the hundredths place this is the tenths place but each tenth is worth 10 hundredths and you see that this is this is you could either view this as seven 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 thousands place so you keep dividing by ten each place you go to the right and you multiply by ten each place you go to the left