When rounding to two decimal places...

well then riddle me this:


1) Round 5.3345 to 3 decimal places. (answer = 5.335)

2) Take your answer from 1 and round it to two decimal places. (answer = 5.34)

3) Why are the answers not the same?





agreed

Do some men really take midol for cramps?

This is much easier to do than it seems. too many people here are using the "equals" term too much. As Burninator has pointed out, it is an Approximation (mmm should learn from his example and learn what equals means before tossing it around so loosely).

Check it out:

5.33 - 5.3345 = abs value .0045

5.34 - 5.3345 = .0055


Hence, 5.33 is a better approximation because it's closer to 5.3345

This is much easier to do than it seems. too many people here are using the "equals" term too much. As Burninator has pointed out, it is an Approximation (mmm should learn from his example and learn what equals means before tossing it around so loosely).

Check it out:

5.33 - 5.3345 = abs value .0045

5.34 - 5.3345 = .0055


Hence, 5.33 is a better approximation because it's closer to 5.3345

Someone needs a hug.


I just though that Burninator nailed it where you had a hard time. You never once said it's an approximation!

Don't hate!




A round number is mathematically defined as the product of a considerable number of comparatively small factors[1] as compared to its neighbouring numbers, such as 24 = 2*2*2*3 (4 factors, as opposed to 3 factors for 27; 2 factors for 21, 22, 25, and 26; and 1 factor for 23).

However, a round number is informally considered to be an integer that ends with one or more zeroes (0), such as 1,000, 1,500,000, etc., and a number ending in 5 might be considered in a way more "round" than one ending in neither 0 nor 5. Even a non-integer such as 2.5 might be seen as more round than, say, 2.497 (especially if written as 2.500).

When a quantity is known only to a low precision, a calculation that gives a non-round number is oftentimes rounded in order to avoid giving a false impression of accuracy.



An approximation is a representation of something that is not exact, but still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.

Approximations may be used because incomplete information prevents use of exact representations. Many problems in physics are either too complex to solve analytically, or impossible to solve using the available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.

For instance, physicists often approximate the shape of the Earth as a sphere even though more accurate representations are possible, because many physical behaviours — e.g. gravity — are much easier to calculate for a sphere than for other shapes.

It is difficult to exactly analyze the motion of several planets orbiting a star, for example, due to the complex interactions of the planets' gravitational effects on each other, so an approximate solution is effected by performing iterations. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained. The use of perturbations to correct for the errors can yield more accurate solutions. Simulations of the motions of the planets and the star also yields more accurate solutions.

Because, your original math problem and the math problem stated above are not the same math problem.

5.3345 rounded to the second decimal equals 5.33

5.3345 rounded to the third decimal equals 5.335

5.335 rounded to the second decimal equals 5.34


* This post was made possible by Math.

You are misquoting me.

5.3345 rounded to two decimal points equals 5.33
5.3345 rounded to three decimal points equals 5.335.
5.335 rounded to two decimal points equals 5.34

But, I'm sure that you have already figured that out by now. So, unless you want to discuss a different issue, I am done explaining this to you.

Maybe you should look up the meaning of equal. I know that rounding is an approximation. However, 5.3345 rounded to the second decimal equals 5.33. I'm using equals because that what it means. It doesn't matter what it "feels" like as another poster keeps saying. Because it is a fact. The word "rounded" in the equation tells you that it is an approximation.

A number that is rounded off is an approximation. I didn't realize that you didn't know that. Sorry about that. I'll try to write future posts in language that you are capable of understanding.



And, for the record, nothing in Burninator's post even referred to my posts. His post was completely accurate and it did not conflict with any of the information that I had posted.

Finally. Some semblance of sanity in this thread of idiocy.
This really isnt rocket science here. Simple rounding that we learn in grade school. Problem is, some people adding steps. "Well this number way past the point that we want to round to is higher than 5 so we round up, which in turn changes this number that is way past the point we are rounding to is now higher than 5 so we round up....."

News flash: 4.344999999999 rounded to the hundredths place is still 4.34

As long as you are convinced what rounded means to you, that's all that matters! regardless what the scientific and mathematical community believes!