Rounding calculations

To what degree are we allowed to round to in the middle of calculations? Here is an example:

c² = a² + b²
c² = 12² + 26²
c² = 144 + 676
c² = 820
c = √820 = 28.63564212655

Now I know the long number in that calculation is the final result but sometimes in questions you will be using long numbers like that half-way through a calculation and it can be real time consuming writing them down repeatedly. Am I allowed to round them to a suitable degree for example 3 decimal places as long as I state that it's 3DP in brackets? Because sometimes if you use rounded figures you end up with a slightly different answer to that in the exam mark scheme.

Many thanks.

Reply 1

Candy_Shop

I would say to keep it as a fraction or root or whatever until the time that you have your final answer ready to round off. Or keep it in the calulators memory.

Reply 2

henryt

You should NEVER round in the middle of calculations; just store the number in your calculator for later if you need to do another seperate calculation. When writing the number on your calc. down on the page, you can skip a few of the digits at the end. Just don't put ≈ anywhere near the middle of your calculations.

If you do go on to do A-level Maths, and esp. Physics, you'll learn the importance of not rounding in the middle of calculations (well - that's what my teacher said!).

Reply 3

Ninja_05

Ah thanks, so for example if I had to write down 23.98736235 I could just write 23.987... to save time?

Reply 4

Guanai

Rounding numbers in middle of calculations won't loose you any marks at all .. if you say to what you have rounded and keep rounding to the same every time e.g to 2 or 3 decimal places ..

Just write next to the number if you have rounded it e.g (2 d.p)

Reply 5

henryt

Rounding to 2 d.p. could potentially make your answer wrong to 3 s.f.. (there's some long proof our teacher did in class).

The actual process of rounding won't lose you any marks; what will, however, is if rounding your working makes your answer wrong at the end of it. 10.5 * 100000 is disctinctly different from 11 * 100000, just to give an (extreme) example.

Also, when using trig functions, rounding can play havoc with your final answer. It's just bad practice to go around rounding stuff randomly.

Round stuff at the beginning of working only if it asks you to estimate, or at the end of a question in other circumstances.

And why bother with rounding 10 times, when you can do it once? :p:

Your calculator can take the "strain" of all of the long numbers!

Also, in answer to question about getting round it, you could avoid using tricky numbers right to the end. For example, if you are asked to write the hypotenuse for a triangle of height and base 1, leave your working as √2. Then at the end of your calculations, your calculator will do all of the hard work, and leave you with probably a very long nasty number, which you can now round. Similarly, use algebra and fractions as much as possible to represent numbers to clear up your page.

For example, if I was asked to work out the volume of a regular square-based pyramid of base length 7, and of slanted height 6, my working would look like this:-

Formula for vol of pyramid = Base area * V. height * 1/3

Base area = 7² = 49

Diagonal base length = √(7² + 7²) = √98, or 7√2, depending on how you do it.

Vertical height = √(6² - (√98/2)²)

Therefore, volume = 49 * √(6² - (√98/2)²) / 3

I would then calculate that, and would save on the writing out of numbers...