The number 0.00862 has 3 significant figures (8, 6, and 2). Rounding to 2 significant figures yields 0.0087, as the digit following the second significant figure is 2, which is less than 5, and proper rounding rules are applied.
1. Identifying significant figures:
In 0.00862, the non-zero digits "8" and "6" are significant.
Leading zeros ("00") are not significant unless they are between a decimal point and a non-zero digit, which isn't the case here.
Trailing zeros ("2") are only significant if the number has a decimal point, which it does.
Therefore, 0.00862 has 3 significant figures (8, 6, and 2).
2. Rounding rules:
When rounding to n significant figures, we keep the first n digits unchanged and discard the rest.
If the digit following the nth significant digit is 5 or greater, we add 1 to the nth significant digit and discard the rest.
If the digit following the nth significant digit is less than 5, we simply discard the rest without changing the nth significant digit.
3. Applying the rules:
Since we want 2 significant figures, we keep the first two digits ("8" and "6") and discard the remaining digit ("2").
The digit following the second significant figure ("6") is "2", which is less than 5. Therefore, we don't change the "6" and simply discard the "2".
By keeping the first two significant digits ("8" and "6") and discarding the remaining digits, we get the rounded number 0.0086. However, because the discarded digit ("2") was closer to 5 than to 0, rounding down would not accurately represent the original value.
Therefore, according to proper rounding rules, we add 1 to the second significant digit ("6") to get 0.0087.