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# Rewriting a fraction as a decimal: 3/5

Sal rewrites 3/5 as a decimal. Created by Sal Khan.

Video transcript

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.