Each of the following numbers was supposed to be rounded to two significant figures. For each one below, decide whether it was correctly rounded or not, and for those that were incorrectly rounded, correct them.
(a) 3.149 e3 to 3.2 e3
Its incorrect but I don't know the correct answer
(b) 7.999 102 to 80
same with this one
50.31 to 50.3
same with this one and I put 50.0 and it said check the number of sig figs
(d) 0.009914 to 0.010
this is incorrect but i don't know the correct one.
thanks:)
im not that good at sig figs:(
The issue you seem to have is not significant figures, but rounding rules.
You can fine rounding rules and examples on a Google search.
a) 3.149e9 rounds (to two sig figures) to 3.1e9
b) 7.999 102 to 80 rounds to 8.0e2
c) 50.31 to 50 or better 5.0e1. When one writes 50, it is difficult to know if the zero is significant, in general it is not. But with 5.0e1, the zero is certain.
d) 0.009914 to 0.0099 is two significant figures.
No problem! I can help you understand how to correctly round numbers to two significant figures.
To determine the correct rounding, we need to follow these rules:
1. If the digit to be dropped is less than 5, we simply remove it.
2. If the digit to be dropped is 5 or greater, we increase the digit preceding it by 1 and remove the rest.
3. If the digit to be dropped is 5 and the digit preceding it is odd, we round up.
4. If the digit to be dropped is 5 and the digit preceding it is even, we round down.
Now let's apply these rules to each of the given numbers:
(a) 3.149e3 to 3.2e3:
Since the digit to be dropped is 4, which is less than 5, we simply remove it. Therefore, the correct rounding is 3.15e3.
(b) 7.999102 to 80:
The digit to be dropped is 1, which is less than 5. Therefore, the correct rounding is 8.0.
(c) 50.31 to 50.3:
The digit to be dropped is 1, which is less than 5. Therefore, the correct rounding is 50.3.
(d) 0.009914 to 0.010:
The digit to be dropped is 4, which is less than 5. Therefore, the correct rounding is 0.00991.
I hope this helps! Let me know if you have any more questions.