Introduction
This interview is based on the game "Hidden Numbers". The interviewer sets up three different comparisons for Caitlin. These show how Caitlin makes decisions about the size of decimal numbers on the length of the decimal part. She generally chooses longer decimals as larger, e.g. she thinks 0.2215 is larger than 0.68. However because Caitlin knows that 0015 is not larger than 68, she first checks that the initial decimal places are not zero.

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

Interviewer:
In this game, you have two mystery numbers and you have to pick the larger one.

In the first game, Caitlin has to compare a decimal with two places with a decimal with four places

Interviewer:
See the decimal point in both numbers?

Caitlin:
I guess the longer one is bigger, unless maybe the whole numbers are different?
I guess I'd better look at those...

Caitlin clicks on the top left hand digit to reveal a 3

Caitlin:
So that number is a three...

Caitlin:
and that number is a three too...So I think the bottom one is bigger because it's longer...Unless there are lots of zeros here

Caitlin:
So if there are zeros there, then maybe they would be about the same...so I'll open this door

Caitlin:
Well that is not a zero, so the bottom number is about one thousand, and the top can't be that big...so I'll choose the bottom number

Caitlin chooses the larger number by accident, but she doesn't know this.

Caitlin:
Great!!!

Many students will not worry about the zeros and would have immediately picked the longer decimal as larger.

Interviewer:
So you want to play another game?

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

Very few students do not know to compare the whole number part of a decimal first.

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

Caitlin:
Ummm... it still could be the bottom one but I think I'll just check here...

Caitlin now thinks she is comparing a three digit number with a two digit number.

Caitlin:
It is the bottom number, because it's about three hundred and the top can't be that big...

Caitlin:
That's funny...I don't know why... Sometimes I get decimals wrong...

Interviewer:
Try another one?

Caitlin:
I'll open these two again to check...

Caitlin:
I'll check here like last time...

Caitlin:
Umm...and open this one...

Caitlin:
This is a really tricky one...I still can't tell...I guess I'll need to open this one...

Caitlin now thinks she is comparing two two digit numbers.

Caitlin:
...and this one...

Caitlin:
I still can't tell! This is a hard one...I'll open this one

Caitlin:
Well 2 isn't very big so it's probably the bottom number again...

Interviewer:
So are you sure about that or do you need to open any more?

Caitlin:
I guess I still need to check this one...

Caitlin:
They're the same!! That was a trick question!!

Caitlin thinks 7.32 is equal to 7.0032 as she has ignored the zeros. She thinks both numbers are 7 with 32 extra bits.