How do I write 96.67673716 with its standard deviation 2.132575 to the correct number of sig figs?
To write a number with the correct number of significant figures (sig figs), you need to consider two things: the number itself and the standard deviation.
First, let's focus on the number 96.67673716. To determine the correct number of significant figures, follow these steps:
1. Count all the digits from the first non-zero digit on the left until the last digit on the right. In this case, there are 11 digits.
2. Remove any trailing zeros if they are not significant. In this case, there are none.
3. If the digit immediately to the right of the last significant digit is less than 5, you round down. If it is 5 or greater, you round up. In this case, the digit following the last significant digit is 1, which is less than 5. So, we don't need to round up.
Therefore, the number 96.67673716, with 11 digits, contains 11 significant figures.
Now, let's consider the standard deviation, which is 2.132575. Standard deviations are typically reported to one more decimal place than the number itself.
Since the number has 11 significant figures, we should round the standard deviation to one more decimal place. In this case, we would round 2.132575 to 2.1.
So, the number 96.67673716, with a standard deviation of 2.132575, rounded to the correct number of significant figures, would be written as 96.67673716 ± 2.1.