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let's see if we can write three-fifths as a decimal I encourage you to pause this video and think about if you can do it on your own and I'll give you a hint here can we rewrite this fraction so instead of it being in terms of fifths it can be in terms of tenths so I'm assuming you've given a go at it let's try to write this as let's try to rewrite this as a fraction with 10 as the denominator but let's just first visualize this so we have fifths so that is one so let's let's say that's 1/5 let me just copy and paste this so copy and paste that is two fists that is 3/5 and that is four ffice and that is 5/5 or if this would be a whole now so that is our whole and we want to color in three of those five so we want to think about what 3/5 are so let me get my magenta out so that's 1/5 I can actually make this bigger even two-fifths and 3/5 there you go color that in that is 3/5 now how could I write this in terms of tenths instead of 3/5 a certain number of tenths well let's split this whole into tenths and the easiest way to split this whole into tenths is to take each of those fifths and turn them into two tenths so let's do that so if we were to just if we were to do this right over here we now have twice as many sections so another way of thinking about it we are taking we are multiplying the number of sections by two we now have ten sections each of these is 1/10 and the three of those sections are now going to be twice as many what we have in magenta we now have twice as many sections in magenta so we're going to multiply that by 2 as well notice we just multiplied the numerator and the denominator by two but hopefully it makes conceptual sense every piece when we're talking about fifth we have now doubled so that instead of everyone v is now 2 is now 2/10 you have a 1/10 now and a 1/10 now and we could just keep writing 1 tens if we like each of these each of these things right over here are a tenth and so and then each of the three are now twice as many tenths so the 3/5 is now 6/10 so let's write that down so this is going to be equal to 6 over 10 6 over 10 now why is this interesting you can literally view this as 6/10 so you could literally view this as 6 let me write it this way 6 times 1/10 6 times 1/10 I'm going to do that in blue 6 times 1/10 well what's another way to represent 6/10 or 6 times 1/10 well you can express that as a decimal where we go to the tenths place so when you write a decimal so let's see zero point the space the the place right to the right of the decimal that is the tenths place this right over here is the ones that right over here is the tenths that's the tenths place so how many tens do we have we have six tenths so we could write this as zero point six so there you have it let me write that this is equal to this is equal to zero point six and we're done we've just expressed this as a decimal 6 tenths is the same thing as six tenths which can be re-written as three-fifths or vice versa