Thread: Rounding off numbers question

OK Guys just a simple question but i can get it through my head.

I want to round off this number to 3 significant digit
18.45056065

Now as far as i know, the rules are
if the two digits following the cutoffpoint is exactly 50 the precedding figure
is not altered if it is an even number.

So following this rule the right answer should be 18.4 right?
The right answer on my book is 18.5. Please help me out!! I cant seem to get why im getting the wron answer! perhaps the book is wrong?

Originally Posted by jepal

OK Guys just a simple question but i can get it through my head.

I want to round off this number to 3 significant digit
18.45056065

Now as far as i know, the rules are
if the two digits following the cutoffpoint is exactly 50 the precedding figure
is not altered if it is an even number.

So following this rule the right answer should be 18.4 right?
The right answer on my book is 18.5. Please help me out!! I cant seem to get why im getting the wron answer! perhaps the book is wrong?

Hmm, you're right about the rule, the answer would be 18.4

But maybe the book does not follow the rule. 'Cause in our Math class, we do not follow that rule, but in our Chem class, we do.

Originally Posted by reiward

Hmm, you're right about the rule, the answer would be 18.4

But maybe the book does not follow the rule. 'Cause in our Math class, we do not follow that rule, but in our Chem class, we do.

its actually for a chem class maybe the book is wrong. I know this is a math forum, so i just assumed the rule would be the same. Any other input?

I do not understand your question. When rounding, if the digit to round is 0, 1, 2, 3 or 4, you round towards the bottom, otherwise you round towards the top.
In your case : 18.45056065, rounded to 3 s.f.
Therefore, you want to round off the first "5". Since it is a 5, it will be rounded towards the top, so the "4" becomes a "5". Hence, the correct answer is 18.5

Originally Posted by Bacterius

I do not understand your question. When rounding, if the digit to round is 0, 1, 2, 3 or 4, you round towards the bottom, otherwise you round towards the top.
In your case : 18.45056065, rounded to 3 s.f.
Therefore, you want to round off the first "5". Since it is a 5, it will be rounded towards the top, so the "4" becomes a "5". Hence, the correct answer is 18.5

There is actually a rule that says when rounding off an even number preceeding the digit "5", you do not add 1 to that number. E.g 18.45 becomes 18.4 ;

It is only applicable though in even numbers.

Then what becomes the "5" ? I've never heard of this rule ... but I must be wrong.

Yet, I need to know why this rule states this particular point before I apply it. Anybody knows ? (or should I make a new thread)

There is no "hard" rule for rounding off number if the digit just after the 'cutoff' is 5.

However, here, since we have many digits given after the 3rd significant digit, you can see that the number 18.45056065 is slightly larger than 18.45 because .00056065 is add to it and so it is slightly closer to 18.5 than it is to 18.4. 18.5 is the correct "round off" as it introduces less error, 0.04943935, than rounding to 184, 0.05056065.