The double squiggle symbol ≈ how did I get this 1.1

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Manu1

Joined Mar 30, 2016
23
Maybe it's worth noting that mathematics is a human construct, an ideal. I once had a math exam question that could be answered numerically, say with 42. I was marked down for doing that, because the professor wanted the symbolic answer. To his way of thinking, using an actual number somehow dirtied the perfection.

Anyone that has worked in the real world knows that a calculated value with a long string of digits is absurd. You can't measure anything that precisely, and your accuracy may be off as well. Two significant figures is typical and more than three starts becoming very difficult.

There's a whole science of how to maintain proper significant figures when adding, multiplying, and averaging numbers. Any introductory text on analytical chemistry would cover it, and I'm sure you could find it in other sources as well.

The about symbol is used to explicitly note that a value has been rounded or approximated for practical reasons. For instance you might write that 3 x 3.3 is about 10. You wouldn't use the equals sign because it would not be technically correct.
Yeah this is a human construction := I don't know how did Indians do this but now we are facing :p
 

amilton542

Joined Nov 13, 2010
497
It means approximately equal.

I use it in trig' , and other occurrences, almost always. For example, I like to express angles in degrees, minutes and seconds because it's a lot more precise and the end user can convert it back to whatever accuracy they choose relevant. But when I use "approximately equal", it's always the end result I will not be substituting.
 

WBahn

Joined Mar 31, 2012
29,979
People use it different ways in different contexts.

It is generally understood that the result of most calculations includes rounding at some point, and so it is very common to see the equality sign used when, strictly speaking, the approximation sign should be used. If the rounding is at a level that is most likely insignificant, then use the equality sign. If the rounding is at a degree such that it is potentially significant for the intended audience, then highlight that by using the approximation sign.

For instance,

\(
\pi^2 \; = \; 9.8696044010893586188344909998762...
\)

but saying

\(
\pi^2 \; = \; 9.87
\)

is generally acceptable since engineering calculations are seldom sensitive to errors on the order of 1% (and this particular error is on the order of 0.004%).

But you will often see this approximated as

\(
\pi^2 \; \approx \; 10
\)

and there you will usually see the approximation symbol used to highlight that the approximation, while very useful, may introduce significant errors (in this case about 1.3%).
 
Last edited:

amilton542

Joined Nov 13, 2010
497
Personally, I don't like rounding off things - - only for the sake of simplicity. The unit of measurement (UOM) you're using could be too significant to even consider rounding up. Imagine rounding up when you're working with tonnes as a UOM!
 

WBahn

Joined Mar 31, 2012
29,979
Personally, I don't like rounding off things - - only for the sake of simplicity. The unit of measurement (UOM) you're using could be too significant to even consider rounding up. Imagine rounding up when you're working with tonnes as a UOM!
I don't see a problem. Rounding does not mean that you are necessarily rounding to an integer. For instance, 31.247 tons might be rounded to 31.25 tons, 31.2 tons, 31 tons, or 30 tons. It all depends on how many sig figs you want and that is pretty much immune to the unit of measure you are using.
 

amilton542

Joined Nov 13, 2010
497
Oh yeah, you're absolutely right! Sig figs! What I should have said was, to the untrained eye you can introduce significant errors. I'll try and dig out this example (I think it involved a recurring decimal if I remember correctly) that makes you pay close attention to mass and rounding-up.
 

MrAl

Joined Jun 17, 2014
11,396
Hi,

Normally the way this is done is if a number to the right is 5 or above, that means the number to the left is increased by 1 and the rest is made zero.

For example, in the number:
3.14159

If we want to round into the form having just two digits like: NN then we would see that we at least need the "3.1". Next, we would look to the right of the 1 and see 4. 4 is less than 5 so we dont increase the 1, and so we just write "3.1" and done.

For the number:
3.15159

we do the same thing, we need at least the "3.1" so we write that:
3.1

and then look to the right of the 1 again, and this time we see a 5, and 5 is equal to 5 so we must increase the 1 to 2 and we get:
3.2

and that is the final result.

For the number 3.16159 we would get the same result 3.2 because that 6 is greater than 5:
3.2

So this isnt too hard to do.

That's the most common way to round in math and engineering so you should use that method. In computer programming it's a little different as sometimes the number is rounded based on the history of previous roundings or a random choice of whether or not to round is imposed to keep the average error over many calculations low.
 
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