1. anonymous

Calculate the above formula, expressing the answer in scientific notation with the correct number of significant figures:

2. Michele_Laino

hint: $\Large 1 \times {10^{ - 3}} = 0.001$

3. Michele_Laino

and: $\Large 3.61 \times {10^{ - 3}} = 0.00361$

4. Michele_Laino

from your attachement I see this computation: $\Large \left( {8.86 + 1.0 \times {{10}^{ - 3}}} \right) \div \left( {3.61 \times {{10}^{ - 3}}} \right)$ am I right?

5. anonymous

Yea you are right. I accidentally read the sign wrong. I was suppose to divide not add. So I should get 2.45429362881 right?

6. Michele_Laino

I got: $\Large \left( {8.86 + 1.0 \times {{10}^{ - 3}}} \right) \div \left( {3.61 \times {{10}^{ - 3}}} \right) = 2.454 \times {10^3}$

7. anonymous

Do I need the full number or should I just shorten it to 2.454?

8. Michele_Laino

I think that we have to take at least 3 significant figures, so our result will be like below: $\Large 2.45 \times {10^3}$

9. anonymous

What exactly are the significant figures? I was confused on that part.

10. Michele_Laino

the significant figures are 2, 4, and 5

11. Michele_Laino

another example: if we have a number like below: 1.0025 then the significant figures are: 1, 2, and 5

12. Michele_Laino

whereas, if we have this number: 1,200 then the significant figures are 1 and 2

13. anonymous

So the signification figures would the answer to that part be 3? Or would the answer to that part be 2, 4, and 5.

14. Michele_Laino

if we have this number: 0.0025 then the significant figures are 2, and 5

15. Michele_Laino

your answer, is: $\Large 2.45 \times {10^3}$

16. anonymous

So with scientific notation you only go 2 digits after the decimal right? I thought the answer was 2.454 x 10^-3. Or am I wrong on that part?

17. Michele_Laino

when we have a decimal point, the significant figures are the figures at the left and at the right with respect to that decimal point

18. Michele_Laino

so, the number 2.454 x 10^-3 has four significant figures

19. Michele_Laino

20. anonymous

I'm not sure what you mean on computation or experimental?

21. Michele_Laino

since 1*10^-3 has only one significant figure, then we have to rewrite our result with one significant figure, so your result is: $\Large 2 \times {10^3}$

22. anonymous

I was just wondering on the scientific noation is both 2.45 and 2.454 both correct. It doesn't matter how I state it. Only difference is how many significant figures their are.

23. Michele_Laino

2.45 has three significant figures, whereas 2.454 has four significant figures

24. Michele_Laino

as a general prescription, we have to round off our result like the most inaccurate measure. Now our most inaccurate number is 1*10^-3 which has only one significant figure. So we have to round off our final result to one significant figure, so we get: $\Large 2 \times {10^3}$

25. anonymous

I'm confused on how I'm suppose to state my answer. How should I write it?

26. Michele_Laino

it is simple, your measure has to be written like below: $\Large 2 \times {10^3}$ which has only one significan figure, and such significant figure is 2

27. Michele_Laino

I have rounded off 2.454... to 2

28. Michele_Laino

please sorry, I see that the most inaccurate number is: 1.0 *10^-3 which has 2 significant figures, so we have to round off our result to 2 significant figures, so your result is: $\Large 2.5 \times {10^3}$ I have rounded off 2.454... to 2.5 and 2.5 *10^3 has 2 significant figures, namely 2, and 5 Sorry again, for my error

29. Michele_Laino

more explanation: a number like this one: 1.0 has two significant figures, namely 1 and 0

30. anonymous

Do I have to round when stating my answer? Does it matter how I state my answer also?

31. Michele_Laino

yes! since when you do a computation, using some formula, the result which you get, can not be as accurate as the most accurate measure

32. Michele_Laino

as a general prescription, the result which you get from a computation has to be as accurate as the less accurate measure

33. anonymous

So how many digits should I state in the answer? Should I round it or not? I normally don't round it unless the question states to do so.

34. Michele_Laino

yes! you have to round it, like below: $\Large 2.5 \times {10^3}$

35. anonymous

So is the answer is 2.5 x 10^3 or 2.5 x 10^-3 @Michele_Laino ? Do you need to take the - off with scientific notation? The original question had a -3 so I wasn't sure. Also for the significant figures there's two of them right? 2 and 5.

36. Michele_Laino

yes! the significant figures are 2 and 5, and the right result is 2.5 x 10^3

37. anonymous

Thanks for all your help @Michele_Laino