Dear Experts,

This is not the type of question normally posted here.
I can't find the answer I hope you can help.
I was told by a math person to ask a physicist, I needed a real true number answer, not a “well, normally people put”, but I want a real what is true in math and numbers.
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

67.467 rounded to the nearest hundredth is 67.47. Your son rounded to the nearest thousandth.

9.017 rounded to the nearest hundredth is 9.02.

Here is a website that may help you. http://www.aaamath.com/g5_44bx1.htm

Adding the 0 made it incorrect, since it took it out of 100th, into 1000th.

Sorry, he needed to drop the 1000th number, the 0 at the end, took it back to the same type of number it used to be.

When "rounding" you stop at the basic number asked for, do not add any additional.

This is very tech difference, but it is a large difference at not following the instructions, exactly as asked.

Fr-Chuck is correct, but to clarify something - adding an extra 0 is incorrect because it means that the number is accurate to three digits past the decimal. For example: his first answer was 67.470, which implies the original number is somewhere between 67.4695 and 67.4705. But it wasn't, so this answer is incorrect. By limiting the answer to only two digits past the decimal it more correctly implies that the original number is between 67.465 and 67.475, which it is.

It may seem a bit subtle, but the number of 0's placed after the last significant digit matters. For example saying that the length of something is, say, 12 inches is different than saying it's 12.00000 inches. The former implies an accuracy of plus or minus 1/2 inch whereas the latter implies an accuracy of plus or minus 0.000005 inches.

Thank you all for your replies.
Some quick questions regarding them.

J 9 : you said he rounded 67.467 to the nearest 1000th, wouldn't that answer be 67.467?

FR Chuck : You said "his answer was 67.470 which implies that the original number was between 67.4696 and 67.4707, but it wasn't". Why would it imply that, if we don't know what the original number was, we don't know if it was rounded up or down, so it could have been between 67.465 and 67.474

ebaines: We make items for Rocketdyne, medical companies, etc.. It's never assumed what the accuracy is unless they specify it, such as +/- .005, but are you saying that by him putting a zero after 67.47 making it 67.470 it implies a higher accuracy? Back to his question, if I say the question different "Is this number 67.47000 rounded to the nearest 100th if the original number is 64.467" would this be correct or not?

Thank you all for your replies.
Some quick questions regarding them.

J 9 : you said he rounded 67.467 to the nearest 1000th, wouldn't that answer be 67.467?

Correct. He did not round to the nearest 1000th.


FR Chuck : You said "his answer was 67.470 which implies that the original number was between 67.4696 [sic] and 67.4707[sic], but it wasn't". Why would it imply that, if we don't know what the original number was, we don't know if it was rounded up or down, so it could have been between 67.465 and 67.474

It was me who wrote that. If the original number was 67.4651, it would round to three places after the decimal poimt to 47.465, not 47.470. Stated another way - given a measurement of 47.470, the plus-or-minus accuracy is 0.0005.


ebaines: We make items for Rocketdyne, medical companies, etc.. It's never assumed what the accuracy is unless they specify it, such as +/- .005, but are you saying that by him putting a zero after 67.47 making it 67.470 it implies a higher accuracy?

Yes. Of course in engineering drawings the accuracy is specified. In math (and especially physics) we use the data with the least number of significant digits to determine the accuracy of the final answer.


Back to his question, if I say the question different "Is this number 67.47000 rounded to the nearest 100th if the original number is 64.467" would this be correct or not?

No, it's incorrect. 64.467 rounded to the nearest hundredth is 64.47, not 64.470000000.

Ebaines: Thanks for taking the time to answer my question and clearing it up.