posting simple question here because I need high intelegence answer.

[ivan1j]

Dear Math Experts,

I can't find the answer to this simple question and I hope you can help.
I'm posting here because I need an answer from people that are experts in math.

My son's test was sent home and all were marked as wrong. The question was Round to the hundredth. After = is what he put.
1.) 67.467 = 67.470, 2.) 9.017 = 9.020, 3.) 43.284 = 43.280, 4.) 16.107 = 16.110 , 5) 5.658 = 5.660

I spoke to the teacher and said they were all correct, he said no he rounded to the 1000th, I said if he rounded to the 1000th the 1st one would be 67.467 he said because he put a zero it's not correct, I said it would not matter how many zero's it's still the same number and is a correct number if rounding to 100th and a number is a number you can't change it or make it different no matter how many zeros.
Am I correct or not?
Thanks

 

[Ishuda]

While it is true that the 67.47 and 67.470 are the same number in a strict mathematical sense, the problem is that if you write, for example, 67.470 you are implying the zero is significant. That is, the value, in an engineering-mathematical sense, is 67.470\(\displaystyle \pm\)0.0005, i.e. a number rounded to the 1000th place. Whereas, if you write 67.47 you are implying 67.47\(\displaystyle \pm\)0.005, i.e. a number rounded to the 100th place. When you talk of rounding numbers, you are talking about numbers in an engineering-mathematical sense so 67.470 is incorrect for a number rounded to the 100th place.