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# Decimal to simplified fraction

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Write 2.75 as a simplified
fraction. So once you get some
practice here. You're going to find it pretty
straightforward to do. But we're really going to think
through it and get the intuition for why this
makes sense. So if we were to write this
down, the 2, that literally just represents two 1's, I'll
just write it down like that. Then we have the 7
in another color. We have a 7 one place to the
right of the decimal. It's in the tenths place,
with a T-H-S at the end. So it literally represents
7 over 10. And then finally, we have the 5
in the hundredths place, so it represents 5 over 100. Now, if I want to write this as
a simplified fraction, or really as a mixed number, I have
to merge these fraction parts right here. And to add two fractions, you
have to have a common denominator. And to figure out the common
denominator, you just have to think about the least common
multiple of 10 and 100. And that's 100. 100 is divisible by
both 100 and 10. So let's get this
10 to be 100. So we can do that by multiplying
it by 10. So when you multiply something
by 10, you add a zero at the end of it. But you can't just do that
to the denominator. We also have to do that
to the numerator. So we multiplied the
denominator by 10. Let's also multiply the
numerator by 10. 7 times 10 is 70,
or 70 over 100. It's the exact same
thing as 7/10. Now we can add these two. What is 70 plus 5? 70 plus 5 is 75. And our denominator is
100, so this can be rewritten as 2 and 75/100. And we saw that in the last
video, you would read this as two and seventy-five
hundredths. Now we aren't in a completely
simplified fraction yet because 75 and 100 have
common factors. And the largest number that
goes into both, if you're familiar with quarters, is 25. Three quarters is $0.75, four
quarters is 100 cents, or four quarters is $1.00. So you divide both
of them by 25. So 75 divided by 25 is 3, and
100 divided by 25 is 4. So as a simplified mixed
number, this becomes 2 and 3/4. And after you do a lot of
practice here, and you just see a lot of numbers like this,
it will be almost second nature for you to say, oh, 2.75
is the same thing as 2 and 75/100, is the same
thing as 2 and 3/4.