Which is greater 3.5 or 0.35?

Answer 1

3.5

Of course just saying the answer is not fun.

Why? For an experienced mathematician it's obvious, but for a elementary, junior high, sometimes even high school students gone "goofed" would ask why?

We need to compare digits starting from the very left, as the on on the very left represents that largest "proportion" of the number. (For instance 123, 1 stands for 100, 2 is 20, 3 is 3 and 100 > 20 > 3, 123 = 100 + 20 + 3)

So luckily the one on the very left for this two numbers are equivalent in terms of what I meant by "proportion". You can determine this by comparing how far is it from the decimal. If two numbers have digits that are same distance (and direction) from the decimal, then they are equivalent in terms of "proportion"

3 is one digit to the left, so is 0. Let's compare them, 3 > 0 (Hope you know that, so I don't have to prove it). Then it's done. 3.5 > 0.35. Think about it, why? If you don't know why, put it in the discussion page. I will explain.

Just for practice, let's do another example

123.5 vs. 7.8

We can see the largest proportion for 123.5 is 100, which is larger than the largest for 7.8, which is 7.

I am using very non formal language, you can only think of it intuitively, put what I said on paper, you get it wrong, or at least not proper.