Introduction
Brad plays the game "Hidden Numbers" twice. He gets correct answers efficiently both times so his misconception about decimal notation is only apparent from his explanations to the interviewer.

Comments: Text in italics
Interviewer: Text in red
Brad: Text other colour

Interviewer:
In this game, you have two mystery numbers and try to guess which is larger.

Interviewer:
See the decimal point in both numbers?

Brad:
I guess I'd better look at the whole numbers

Brad:
So that is a three...

Almost everyone knows to compare whole number parts first.

Brad:
and that's a three too...So I think the bottom number is bigger because it's longer, so there would be more tenths...Unless there is a zero here

Brad:
Because if there is a zero just after the point, then that would make them hundredths which is less than tenths.

Brad:
Because it's not a zero, there are tenths in the bottom number and lots of them. I guess I should check whether the top is tenths or hundredths,...no I don't need to, because it can't be as many tenths anyway, so it must be smaller. I'll choose the bottom number as the biggest.

Brad:
Great!!!

Brad has made the right choice but for the wrong reason.

Interviewer:
So here is another pair of numbers.

Brad:
Yes...I'll just check the first numbers.

Brad:
So, I think it will be the bottom number again...I'll just check this door after the point...

Brad:
Well that makes hundredths, so I think the top number is bigger...unless it has a zero too! I'll open this door...

Brad:
That's not a zero so they're tenths, ...so the top number is bigger.

Interviewer:
What would you have done if it was a zero there?

Brad:
Well, if they've both got zeros at the start then they're both hundredths, but you'd really need to check for any more zeros in case they were actually thousandths.

Interviewer:
OK. You chose the top number, didn't you - check if it's bigger.

Brad:
Great!!!

Brad's misunderstandings could easily go undetected by his teacher. Careful listening is important.