Writing decimals and fractions from number lines

We're told to express the point on the number line as both a fraction and a decimal, so pause this video and have a go at that.

All right, now let's do this together. We can see that the point in question is at a higher value than four and less than five. So, greater than four, less than five. The space between four and five is divided into one, two, three, four, five, six, seven, eight, nine, ten equal sections. Each of these hash marks represent an extra tenth.

So this is four, then this is 4 and 1/10, and now this is 4 right over here and two tenths. We could write this, if we wanted to write it as a fraction or as a mixed number, this would be four and two tenths.

If we wanted to write that as a decimal, that would be four, and then in the tenths place, well we have two tenths. And that's it; we're done.

Let's do another example. Here we're once again asked to express the point on the number line as both a fraction and a decimal, but this one's a little bit different. See how you can identify how it is different and answer the question. So pause this video and once again have a go at it.

All right, so here our point is not between two whole numbers; it's actually between two tenths, between 3 and 2 tenths and 3 and 3 tenths. So this is between 3 and 2 tenths and 3 and 3 tenths. Each of these hash marks, which are a tenth of a tenth, would actually be a hundredth.

One way to think about it: you could view 3.2, or 3 and 2 tenths, as 3 and 20 hundredths, and you could view 3 and 3 tenths as 3 and 30 hundredths. So this is 3 and 20 hundredths, this is 3 and 21 hundredths, three and twenty-two hundredths.

So this point right over here is 3 and 22 hundredths. Of course, you could also write that as a mixed number; that is 3 and 22 over 100. Now, another way that you could have approached it is, hey, I'm starting at 3.2 or 3 and 2 tenths, so I'm starting here at 3.2, and then I'm going to add to that not just one hundredth, but two hundredths.

So it would be three, two tenths, and then two hundredths, and there you have it. We've expressed it as both a fraction and a decimal.