A question about significant digits of digits in parentheses at the end

In summary, the value of Avogadro's number is 6.022 141 29(27)x10^23. The parentheses at the end indicate the error in the measurement, with the number within representing the best determined value and the number outside representing the uncertainty. To preserve the proper number of significant digits, the number within the parentheses is rounded to the nearest half of the error value. However, the most accurate value would include the exact uncertainty, which is not shown here.
  • #1
swampwiz
571
83
I was looking at the value of Avogadro's number

6. 022 141 29(27)×1023

and was trying to figure out what exactly is meant by the parentheses at the end. I'll take a guess and say that the best determined value has these digits, but that the error is high enough so that only by using the number before the parentheses, with its default error of being +/- 1/2 of the value of the last digit place (i.e., here .000 000 01×1023) can the proper number of significant digits be preserved.

Obviously, the most descriptive value would be the one that has the exact amount of uncertainty, but it is not presented here.
 
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  • #2
It means 6.022 141 29 * 10^23 +/- 0.000 000 27 * 10^23
 

1. What are significant digits and why are they important?

Significant digits are the digits that carry meaning in a number. They indicate the precision or accuracy of a measurement or calculation. It is important to pay attention to significant digits in order to correctly convey the accuracy and precision of a value.

2. How do you determine the number of significant digits in a number?

The general rule for determining the number of significant digits is to count all non-zero digits and zeros between non-zero digits. Trailing zeros after a decimal point are also significant. For example, in the number 3.045, there are four significant digits.

3. What is the significance of digits in parentheses at the end of a number?

Digits in parentheses at the end of a number are often used to indicate uncertainty or estimated values. They are not considered significant digits and should be treated as such in calculations.

4. How do you perform calculations with significant digits?

In addition to following the general rule for determining significant digits, there are specific rules for addition/subtraction and multiplication/division. When adding or subtracting, the result should have the same number of decimal places as the least precise number. When multiplying or dividing, the result should have the same number of significant digits as the least precise number.

5. Why is it important to properly round numbers based on significant digits?

Rounding numbers based on significant digits is important because it ensures that the final result reflects the precision and accuracy of the original values. Improper rounding can lead to significant errors in calculations and can affect the validity of scientific data.

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