Converting decimals to fractions example 1 | Decimals | Pre-Algebra | Khan Academy

We're practicing how to convert a lonely decimal into a happy fraction.

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Let's see if we can
write 0.15 as a fraction.

So the important
thing here is to look

at what place these
digits are in.

So this 1 right over here,
this is in the tenths place,

so you could view
that as 1 times 1/10.

This 5 right over here is
in the hundredths place,

so you could view
that as 5 times 1/100.

So if I were to rewrite
this, I can rewrite this

as the sum of-- this 1
represents 1 times 1/10,

so that would literally
be 1/10 plus--

and this 5 represents
5 times 1/100,

so it would be plus 5/100.

And if we want to
add them up, we

want to find a
common denominator.

The common denominator is 100.

Both 10 and-- the
least common multiple.

100 is a multiple
of both 10 and 100.

So we can rewrite this
as something over 100

plus something over 100.

This isn't going to change.

This was already 5/100.

If we multiply the
denominator here

by 10-- that's what we did;
we multiplied it by 10--

then we're going to have to
multiply this numerator by 10.

And so this is the
same thing as 10/100.

And now we're ready to add.

This is the same thing
as-- 10 plus 5 is 15/100.

And you could have done that
a little bit quicker just

by inspecting this.

You would say, look, my
smallest place right over here

is in the hundredths place.

Instead of calling this
1/10, I could call this

literally 10/100.

Or I could say this
whole thing is 15/100.

And now if I want to reduce
this to lowest terms,

we can-- let's see, both the
numerator and the denominator

are divisible by 5.

So let's divide them both by 5.

And so the numerator,
15 divided by 5, is 3.

The denominator, 100
divided by 5, is 20.

And that's about as
simplified as we can get.