Significance of 7 in 1.00794(7), Parentheses Notation in Statistics

In this article we shall understand about the parentheses notation that is used in statistics to express the uncertainty. 

for example, 

1.00794(7)

What does 7 within the first bracket signifies? 

Reading the Parentheses Notation

• The number in parentheses applies only to the last digits of the number.

• Example:

  • 1.00794(7) means 1.00794 ± 0.00007.

  • 1.00794(72) means 1.00794 ± 0.00072.

• This format is used by IUPAC for atomic masses and in scientific measurements.

Molar Mass of Iridium

192.21662(29) g/mol means:  

Measured value = 192.21662 g/mol 

Uncertainty = ±0.00029 g/mol

How to Interpret It?

• The uncertainty (29) affects only the last two digits of 192.21662.

• This means the actual value is somewhere between 192.21633 and 192.21691 g/mol.

Radioactive Decay Half-Life

• Half-life = 670(102) s

  • This means the value is 670 seconds ± 102 seconds.

  • The actual value is somewhere between 568 s and 772 s.

• Lifetime = 967(147) s

  • This means 967 seconds ± 147 seconds.

  • The range is between 820 s and 1114 s.

Gist

• Parentheses indicate uncertainty in the last few digits of the number.

• The numbers in parentheses represent the 1σ uncertainty 
  

• The larger the number in parentheses, the greater the uncertainty in the measurement.

• This notation is used in high-precision scientific studies, such as physics and metrology.

Reference

All are included in the text as hyperlink

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