Expressing decimals in multiple forms

We're asked which two of the following expressions have the same value as eight point seven six. Pause this video and see if you can figure this out on your own.

Alright, now let's do it together. Before I even look at these choices, I'm just going to really understand what this number represents. Let me just rewrite it, so we have eight point seven six.

So there's a couple of ways that we could think about it. We can look at our place values. This right over here, this is the ones place. This right over here, this is the tenths place. And this right over here is the hundredths place.

So we could view this as eight ones and seven tenths and six hundredths, or eight ones plus seven tenths plus six hundredths. Well, that's exactly what they wrote right over here: eight ones, seven tenths, and six hundredths. So I would choose that one for sure.

Now, this second choice looks like an expanded form. But before I even look at it, let's see how we would think about it over here. If we wanted to essentially write the same idea but in expanded form, eight ones is the same thing as eight times one.

Actually, let me color code it so you see where things are coming from. So, eight ones—that's the same thing as 8 times one, and then we would add seven tenths, so that's plus seven times 1/10. So, seven tenths plus—and I'll do this in this orange color—six hundredths, so that's plus six times one-hundredth.

This number in expanded form, is that what they put right over here? Yes, it is indeed what they put right over here, so I will circle that in.

Now, if you're doing this on your own, we know that we just picked two answers, but let's see whether these other forms—or let's see if we can write this in these other forms and see how these might not be the exact answer.

So if we were to write this out and take out each of the decimal parts—so the eight ones—you would just write that as eight. The seven tenths—that would be plus 0.7.

This is seven tenths right over here. This and this and this part right over here are all equivalent. And then last but not least, you have your six hundredths, so that's plus—so that's our ones, that's our tenths, and they're not wearing a hundredths place, and we're gonna have six of them.

So this would be equal to our original value, but that's not what they wrote over here. They did write eight ones, they did write seven tenths, but they did not write six hundredths here; they wrote six thousandths here, so we can rule that one out.

Then, if we were to write it out in words, we would say this is eight—eight—and I'll do in a neutral color. Now you might say "and seven tenths and six hundredths," or you could often—what's normally is you express it in the lowest place that you have, or the most precise place that you have.

So you could view seven tenths as seventy hundredths, or you could view this whole thing as seventy-six hundredths. So it could be eight and seventy-six hundredths. But what they wrote over here, they did write eight, but instead of seventy-six hundredths, they wrote eight and sixty-seven hundredths—a little tricky! So we would rule that one out as well.