I finished Chapter 8 on rounding decimals for the latest version of How to Help Your Child with Fifth Grade Mathematics that I uploaded on July 5th, 2013.
This is one of those standards that does confuse some fifth grade students. I have always connected it to our base ten number system, and try to make it really clear to students why we round the way that we do.
That said, I have long found it confusing, though, in how we talk about rounding “up” and rounding “down”.
For example, 0.43 rounded to the nearest tenth is 0.4. We describe that as rounding “down”, but we don’t round the 4 in the tenths place “down” to a 3. It remains as a 4.
On the other hand, if we round 0.47 to the nearest tenth, then we do round it “up” to 0.5. In this case, the 4 in the tenths place does move “up” to the next largest digit, a 5.
As I was writing the chapter, it occurred to me that if we think of the whole number, rather than just that relevant digit, then rounding “up” and rounding “down” makes more sense.
Let’s take the numbers from 0.40 to 0.49. If we round each of them to the nearest tenth, then half of them, five, will round down to 0.4, while the other half will round up to 0.5.
The numbers 0.40 to 0.44 will round down to 0.4, while 0.45 to 0.49 will round up to 0.5.
I’m glad I wrote this chapter, because in thinking more about rounding numbers and how to explain that procedure, I clarified for myself something that has confused me about the language we use. In one context, it could be confusing. And I will still address that possible confusion with my students. In another context, it makes sense that we talk about rounding up and rounding down.