Examples writing decimals and fractions greater than 1 shown on grids

We're told each big square below represents one whole. Express the shaded area as both a mixed number and a decimal. So pause this video and see if you can do that. What would this be as a mixed number, and then what would it be as a decimal?

All right, now let's do it together. So let's first start with the mixed number. We see that we have one whole here. The whole thing is filled out, so this is going to be one whole.

Then over here, we have part of this second whole filled out, and it looks like we are dividing this whole into ten equal sections, and then two of those are filled out. So as a mixed number, we have one, and then you have two of the tenths filled out. So this is going to be one and two tenths, and we're done. You can see here this is split into tenths, and we filled in two of them.

Now what about as a decimal? Well, we could just express one into tenths as a decimal. We could say, "Hey, that's going to be one," and then we get to the tenths place, and then how many tenths do we have? We have two of them, so that's going to be one point two.

Let's do another example. So here this is a little bit more involved. They say once again each big square below represents one whole, and once again they want us to express the shaded areas both as a fraction and a decimal. So pause this video and have a go at this.

All right, so let's start with a fraction again. So we have one whole, two holes, and then partially shaded in this third hole. So if I'm going to express this as a fraction, it really is going to be a mixed number. I would say that this over here, this is two wholes.

Now this third hole is only partially filled in, and we can see that it has been divided into hundredths. You can see it's a 10 by 10 grid, so each of these squares represents one hundredth of a whole. How many of these hundredths are filled in? Well, let's say you have 10, 20, 30, 40, 50, 60, 70, and then you have 70, one, two, three, four. We can see that seventy-four of the hundredths are filled in.

So as a mixed number, this whole thing would represent two and seventy-four hundredths. Now, if we want to write it as a decimal, we would have two holes, and then we could go to the tenths place. You could just write two and seventy-four hundredths like that.

If you're pretty familiar with it, you could also think about it in terms of how many tenths and how many hundredths do you have. We have one, two, three, four, five, six, seven tenths, and then we have four more hundredths beyond that.

You could think of it as seventy-four hundredths or seven tenths and four hundredths, but either way, we are done.