Rewriting a fraction as a decimal: 21/60

Let's see if we can write 21/60 as a decimal. And I'll give you a little hint. See if you can rewrite this as a fraction with 100 as the denominator. Or another way to say it is see if you can rewrite this so it's a certain number of hundredths, and then you can represent that as a decimal. So we've done this before. We can rewrite a fraction. We can get an equivalent fraction if we either multiply the numerator and the denominator by the same quantity or we divide the numerator and the denominator by the same quantity. And this numerator and this denominator, it looks pretty clear. 21 is divisible by 3 and 7 and 1 and 21. And 60 is clearly divisible by 3 as well. It's not divisible by 7 or 21. Well, of course, it's divisible by 1, but that doesn't really help you much. So let's see if we can rewrite this, maybe with lower numbers, where we divide both the numerator and the denominator by that common factor of 3. So we're dividing by 3. So I'm just rewriting this as an equivalent fraction that might make it a little bit easier for our heads to get around it. So 21 divided by 3 is equal to 7. And 60 divided by 3 is equal to 20. So we've rewritten 21/60 as 7/20. So you might be saying, Sal, why did you even do this? Aren't we trying to get it in terms of hundredths? Well, this one helps simplify it in my brain a little bit. And what's extra good about writing it as 7/20 it is that it's easier to go from 20 to 100. To go from 20 to 100 we just have to multiply by 5. Well, if each section is going to be five times as many then these seven sections are going to be five times as many. So, once again, we're multiplying the numerator and the denominator by the same thing. And so this is going to be equal to 35 over 100, or 35/100. 35-- let me write it a little bit-- 35/100, which is what we wanted to do. We wanted to rewrite this in terms of hundredths. And what is 35/100? Well, let's just remind ourselves when we're writing a decimal, that's the ones place. This right over here, this next place, is the tenths place. And the next place is the hundredths place. And so 35/100, well, you could write that like this. You could write that as 35 hundredths. So you could literally write this as 0.35. And you might say, wait, you put a 3 in the tenths place. Why is this 35 hundredths? I get that this is 5 hundredths, but why is this 35 hundredths? Well, 3/10 is 30/100. So this is 35/100. Or another way of thinking about it, you could rewrite this right over here. You could rewrite this as being equal to 30/100 plus 5/100. And what is 30 over 100 if you wanted to rewrite it in terms of tenths? Well, you could just divide the numerator and the denominator by 10, and you would get 3/10 plus 5/100. And we see that right over here, 3/10, that's the tenths place, plus 5/100, that's hundredths place. Or this is sometimes referred to as 35/100.