Rewriting decimals as fractions: 0.15

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.