Round Negative Numbers - Significant Digits Questions

  • Thread starter brad sue
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In summary, when rounding negative numbers, the same rules apply as rounding positive numbers. For example, -8.46 to two significant digits would be rounded to -8.5 because the "6" makes it closer to -8.5 than -8.4. Additionally, when rounding to a certain number of digits, such as 4, only the next digit is used. For instance, 3816.512 rounded to 4 significant digits would be 3816 and -3816.512 would also be rounded to -3816. Similarly, 256453 rounded to 3 significant digits is 2.56x10^5. It is important to use scientific notation to avoid misleading results, as rounding to a
  • #1
brad sue
281
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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
 
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  • #2
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.
 
  • #3
HallsofIvy said:
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
 
  • #4
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.
 
  • #5
danim said:
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".
 
  • #6
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.
 

FAQ: Round Negative Numbers - Significant Digits Questions

What are round negative numbers?

Round negative numbers refer to the process of simplifying or approximating a negative number to a certain degree of accuracy. This is often done to make the number more manageable or to follow a certain set of rules or guidelines.

How do you round negative numbers?

To round a negative number, you follow the same rules as rounding positive numbers. If the digit to the right of the desired decimal place is 5 or greater, you round up. If it is 4 or less, you round down. For example, if you want to round -4.567 to the nearest whole number, it would become -5. If you want to round -4.567 to the nearest tenth, it would become -4.6.

What are significant digits in round negative numbers?

Significant digits, also known as significant figures, refer to the meaningful digits in a number. In round negative numbers, the significant digits are the digits that are used to determine the rounding process. For example, if you want to round -4.567 to three significant digits, the answer would be -4.57 because the 3 and 7 are the first three significant digits.

When do you use significant digits in rounding negative numbers?

Significant digits are used in rounding negative numbers when you want to maintain a certain level of accuracy in the rounded number. This is especially important in scientific calculations and measurements, where the precision of the result is crucial. By using significant digits, you can ensure that the rounded number is as accurate as possible without introducing any extra digits.

Can you round negative numbers to any decimal place?

Yes, you can round negative numbers to any decimal place. The number of decimal places you choose to round to will depend on the level of accuracy you need for your calculations. Just remember to follow the same rounding rules as you would with positive numbers, and to consider the significant digits when rounding to a specific decimal place.

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