Rewriting a fraction as a decimal: 3/5

Let's see if we can write 3/5 as a decimal. And 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 rewrite this as a fraction with 10 as the denominator. But let's just first visualize this. So we have fifths. So let's say that's 1/5. Actually, let me just copy and paste this. That is 2/5. That is 3/5, and that is 4/5. And that is 5/5, or this would be a whole now. So that is our whole. And we want to color in 3 of those 5, 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-- 2/5 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 2/10. So let's do that. So 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 multiplying the number of sections by 2. We now have 10 sections. Each of these is a tenth. And the 3 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 2. But hopefully it makes conceptual sense. Every piece, when we're talking about fifths, we've now doubled so that instead of every 1/5 is now 2/10. You have a 1/10 now and a 1/10 now. And we could just keep writing 1/10 if we like. Each of these things right over here are a tenth. And then each of the 3 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 6/10. Now why is this interesting? You can literally view this as 6/10-- let me write it this way-- 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 0 point-- 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 tenths do we have? We have six tenths. So we could write this as 0.6. So there you have it. Let me write that. This is equal to 0.6. And we're done. We've just expressed this as a decimal. 0.6 is the same thing as 6/10, which could be rewritten as 3/5 or vice versa.