Is $ 5 $ nearer to $ 0 $ or $ 10 $?

My 6-year-old’s homework was “to find the nearest $ 10 $.” For example, $$ 42 \to 40 \quad \text{and} \quad 28 \to 30. $$ For $ 55 $, she answered “$ 50 $” and was marked wrong. How is this wrong? Clearly, $ 55 $ is slap-bang in the middle of $ 50 $ and $ 60 $, so surely either answer is correct. The question does not mention rounding of any sort, therefore you can’t say that common rounding is being used. Comments are most welcome!

Solution 1:

$$|55-50|=5 \\ |55-60|=5 \\ 5=5$$ QED

Solution 2:

I would agree with you that both answers should be correct. Despite your plea not to mention common rounding, I suspect that is where the problem is-the answer key was made up with "round 5 to even" or "round 5 up" in mind.

Solution 3:

This is probably an exercise on rounding, where if the one's place is greater than or equal to $5$, then rounding up is considered "correct" (although if you study statistics at a high level, you will find out that this is not the case; there are different rules). However, the question said "find the nearest", in which case both answers are correct. The question in the homework is pretty ambiguous, and IMHO should not be asked.

Getting back to the main question, let's examine the differences between $0$ and $5$, and $5$ and $10$.

$0$ is exactly $5$ away from the number $5$, and so is $10$. The number $5$ is right in the middle of $0$ and $10$. It is not closer to any of the numbers.

$$\underbrace{0, \ 1, \ 2, \ 3, \ 4,}_{\text{5 numbers}} \ \mathbf 5, \ \underbrace{6, \ 7, \ 8, \ 9, \ 10}_{\text{5 numbers}}$$

Imagine a race is held in a $10\text{km}$ straightaway. One car starts at the very left (i.e. at $0$ km) and the other starts at the very right (i.e. at $10$ km). Both cars have to travel $5$ km to the finish line. If they both travel at the exact same speed throughout the race, then obviously they will get there in the exact same time!

The point of that was to say that the difference between $0$ and $5$, and $5$ and $10$ are the same! There's no "$0$ is closer to $5$" or any of that stuff.

$5$ is as close to $0$ as it is close to $10$.

Solution 4:

You're right that it's ambiguous so there is a long-standing convention that you always round the 5 up.