Round Negative Numbers - Significant Digits Questions

[brad sue]

Hi ,
I have a quick question about significant digits number
what is -256453 rounded at 3 significant digits?
what is -3816.512 rounded at 4 significants digits?
I am confused when I have to rounded negative numbers.
Can someone help me please?
B

 

[HallsofIvy]

You round negative numbers the same way you round positive numbers!

8.46 to two significant digits is 8.5 because the "6" makes it closer to 8.5 than 8.4.

-8.46 to two significant digits is -8.5 because the "6" makes it closer to -8.5 than -8.4.

256453 rounded to 3 significant digits is 256000 and -256453 rounded to 3 significant digits is -256000.

3816.512 rounded to 4 significant digits is 3816 and -3816.512 rounded to 4 significant digits is -3816.

 

[danim]

3816.512 rounded to 4 significant digits is 3816 and -3816.512 rounded to 4 significant digits is -3816.

Sorry, I think you mean +/- 3817, because .51 > .5

 

[JonahHex]

When rounding to a certain number of digits (eg 4), ONLY the next digit (the 5th) is used, ie, 3816.512 to 4 sig figs is 3816, the '1' following the '.5' is immaterial.

256453 rounded to 3 sig figs is 2.56x10^5, not 256000. Including the zeros is misleading and potentially implies that they have some meaning, which they do not. It is not possible to ascertain, by simply looking at the final number, that the zeros are merely place holders.

 

[HallsofIvy]

Sorry, I think you mean +/- 3817, because .51 > .5

One can argue that. Some texts follow a rule that if the next digit is 5, regardless of what the digit after is, you round to the nearest even digit. That's because, of course, at .5 you are going to be making about as large an error as you can however you round. If you always round to the even digit, about half the time you will round up, half the time down. If you are rounding a large set of numbers, the errors will tend to offset.

As JonahHex said, rounding -256453 to three significant figures as
-256000 can be misleading since you don't know whether the "0"s are "significant" or not: -256034 rounded to 4 significant figures would also be -256000. Better is -2.56x10⁵ and -2.560x10⁵. That's one of the main reasons for using "scientific notation".

 

[JonahHex]

The 'even number' explanation is the way I learned it...with one modification: YOU can choose to round 'next digit 5' either odd or even as long as once you make the choice you subsequently ALWAYS follow your own rule; virtually everyone choses to round even.

The .51 argument is specious. The purpose of rounding to a certain number digits has to do w/ the fact that the 'next digit', the one that determines how you round, is obtained by estimation in the original measurement and is thus uncertain. Therefore, if that digit is uncertain, any subsequent digits are actually unknown and meaningless.