Thread: approximations

I dont know how to differentiate an integer from a decimal value which is approxiamtely equal to the integer. I mean we can never measure anything accurately. We tend to round off the figures to nearest integers if possible. The concept of an absolute value like 3 or 7 is unthinkable. I think these are ideal values which are never attained while measuring.

If you are attempting to measure something which has a continuum of possibilities (like your weight), then you can never get an exact value. However if are counting something (like how many dollar bills in your wallet), then you can get an exact value.

You may like to read my article "Telling lies to describe truth: Do we emphasize the importance of “the art of approximations” to the students?" available at link deleted

Mamidala, it is not the purpose to this forum to provide you with a free advertising platform for your site. I trust you understand why. See your other duplicate thread for a fuller explanation. Further repeats of your post will be deleted completely.

It depends on the magnitude of the number.
For measuring something that can have any non-negative real value, if your measurement is from 0 - 10 (relatively small), you need to be more accurate. However, as the numbers get bigger you don't need as many figures. The accuracy with respect to the difference shrinks, but the accuracy with respect to the quotient does not. If you are not sure what this means, please ask and I will explain.
It personally doesn't bother me that continuum real-world measurements can rarely be exact (there are a few, which are DEFINED measurements). Possibly we could get exact answers considering the planck scale says that space, time, mass, and energy are NOT infinitely divisible.

Originally Posted by mathman

If you are attempting to measure something which has a continuum of possibilities (like your weight), then you can never get an exact value. However if are counting something (like how many dollar bills in your wallet), then you can get an exact value.

But the value of the dollars is constantly changing :-)

@anticorncob, you're talking about absolute differences. 1 is a huge difference if your range is between 2 and 4, but a tiny difference if your range was 2000 to 4000. That's why most scientists use relative differences. Both significant figures and scientific notation make use of this somewhat indirectly. 23456 to two significant figures would be 23000, while 0.023456 to two significant figures would be 0.023. In scientific notation the two rounded numbers would be 2.3 * 10^4 and 2.3 * 10^-2. The number of figures doesn't need to change based on the scale involved.