Are Significant Figures Really That Important?

  • Thread starter nobahar
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In summary, significant figures are used to indicate the precision of a number, however they can be affected by unknown numbers in smaller power of ten columns. Thus, calculations using significant figures should not be considered entirely accurate. This is illustrated by the example of y=1/(2-x), where even though x was known to 3 sig figs, y was only known to 1 sig fig due to the unknown number in the calculation.
  • #1
nobahar
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Hello!

I've used significant figures without really thinking about them too much; and I have never really understood there use.
I found this thread: https://www.physicsforums.com/showthread.php?t=477786&highlight=significant+figures

Where it has been argued that they should be 'taken lightly', so to speak.

Here's where I have always been confused, and I hope someone can help!:

If I were to perform the multiplication, 2.09*3.52, I have three significant figures in both numbers, and so the answer would be 7.36 (from 7.3568).
I think this example shows one issue, and that is that the 6 is not necessarily 'known'.
Indeed, depending on the numbers in the multiplication, digits in higher powers of ten columns can be affected by 'unknown' numbers in smaller powers of ten columns. So when a number is given to x significant figures, these numbers may not be the actual numbers!, since they can be influenced by unknown numbers of smaller magnitudes of ten e.g. 1/10th column, 1/100th column, etc can affect the value in the 100 column or the 101 column, etc.
So when I see some calculation using significant figures, I should not necessarily believe any of the numbers are absolutely certain?

I hope that makes sense!
Thanks in advance.
 
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  • #2
if we say x=1.97, then it is taken as being between 1.96 and 1.98

consider the equation, y=1/(2-x)

If x=1.96, then y=25
if x=1.98, then y=50

so, we have found, y=37 +/- 13

Summarizing, although x was known to 3 sig figs, y is known to not much better than 1 sig fig.

Does this illustrate what you were talking about?
 
  • #3
NascentOxygen said:
if we say x=1.97, then it is taken as being between 1.96 and 1.98

consider the equation, y=1/(2-x)
...
Summarizing, although x was known to 3 sig figs, y is known to not much better than 1 sig fig.

Yes, but clearly the problem step was (2-x), which left you with 0.03, known to one sig fig. The OP's example had only multiplication, which tends to be less tricky.
 

FAQ: Are Significant Figures Really That Important?

What are significant figures (sig figs) and why are they important in science?

Significant figures are the digits in a number that carry meaning or contribute to the precision of a measurement. In science, they are important because they help us understand the accuracy and precision of our measurements and calculations.

How do I determine the number of sig figs in a measurement?

To determine the number of sig figs in a measurement, start by identifying the certain digits, or non-zero digits, in the number. Then, count all the digits after the certain digits until you reach the first uncertain digit, which is usually a zero. The number of certain digits plus the first uncertain digit is the number of sig figs in the measurement.

3. What is the rule for rounding when dealing with sig figs?

The general rule for rounding with sig figs is to round the uncertain digit to match the number of sig figs in the measurement. If the uncertain digit is less than 5, round down. If it is 5 or greater, round up.

4. Can I use sig figs in calculations?

Yes, sig figs can and should be used in calculations. The final answer should have the same number of sig figs as the measurement with the least number of sig figs in the calculation. Intermediate steps in the calculation should be done with more sig figs to avoid rounding errors.

5. How do I know when to use decimal places instead of sig figs?

Decimal places are used when the exact value of a number is known, such as in conversions or when working with defined constants. Sig figs are used when the value is measured or calculated and has some degree of uncertainty.

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