Significant Figures -- Rounding

1. Significant Figures -- Rounding So you are now able to determine how many significant figures there are in a given measurement. One related skill that you will need this year is how to round off a given number.

2. Significant Figures -- Rounding 763.48 cm has five significant figures. What would 763.48 cm be rounded to four significant figures?

3. Significant Figures -- Rounding 763.48 cm has five significant figures. What would 763.48 cm be rounded to four significant figures? To answer this question, simply look at the first four significant figures in the number: 763.48 cm.

4. Significant Figures -- Rounding 763.48 cm has five significant figures. What would 763.48 cm be rounded to four significant figures? To answer this question, simply look at the first four significant figures in the number: 763.48 cm.

5. Significant Figures -- Rounding 763.48 cm has five significant figures. What would 763.48 cm be rounded to four significant figures? To answer this question, simply look at the first four significant figures in the number: 763.48 cm. The last one (the “4”) is followed by a big digit (an “8) so the “4” rounds up to a “5” giving us 763.5 cm. And that is the answer.

6. Significant Figures -- Rounding What would 763.48 cm be rounded to three significant figures?

7. Significant Figures -- Rounding What would 763.48 cm be rounded to three significant figures? To answer this question, simply look at the first three significant figures: 763.48 cm.

8. Significant Figures -- Rounding What would 763.48 cm be rounded to three significant figures? To answer this question, simply look at the first three significant figures: 763.48 cm.

9. Significant Figures -- Rounding What would 763.48 cm be rounded to three significant figures? To answer this question, simply look at the first three significant figures: 763.48 cm. The last one (the “3”) is followed by a small digit (a “4), so the “3” rounds down – that is, it stays a “3” – giving us 763 cm. And that is the answer.

10. Significant Figures -- Rounding By the way, a small digit is anything less than “5” (so: 0, 1, 2, 3 or 4). A large digit is anything greater than “4” (so 5, 6, 7, 8 or 9).

11. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures?

12. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm.

13. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm.

14. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm. The “6” is followed by a “3”, so the “6” rounds down – that is, it stays a “6.” But the answer is not what you are thinking!

15. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm. The “6” is followed by a “3”, so the “6” rounds down – that is, it stays a “6.” But the answer is not what you are thinking! It is not 76 cm. Can you figure out what it should be?

16. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm. The “6” is followed by a “3”, so the “6” rounds down – that is, it stays a “6.” But the answer is not what you are thinking! It is not 76 cm. Can you figure out what it should be? It should be 760 cm.

17. Significant Figures -- Rounding What would 763.48 cm be rounded to two significant figures? To answer this question, let’s look at the first two significant figures: 763.48 cm. The “6” is followed by a “3”, so the “6” rounds down – that is, it stays a “6.” But the answer is not what you are thinking! It is not 76 cm. Can you figure out what it should be? It should be 760 cm. The “0” is needed as a place-keeper to keep the “7” in the hundred’s place and the “6” in the ten’s place.

18. Significant Figures -- Rounding If someone owed you $763.48, and all they had was to give you was $760, you would probably be OK with that.

19. Significant Figures -- Rounding If someone owed you $763.48, and all they had was to give you was $760, you would probably be OK with that. If, on the other hand, all they had to give you was $76, you probably would not be OK with that!!!

20. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure?

21. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm.

22. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm.

23. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm. The “7” is followed by a “6”, so the “7” rounds up to an “8.”

24. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm. The “7” is followed by a “6”, so the “7” rounds up to an “8.” But the answer is obviously not 8 cm. Can you figure out what it should be?

25. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm. The “7” is followed by a “6”, so the “7” rounds up to an “8.” But the answer is obviously not 8 cm. Can you figure out what it should be? It should be 800 cm.

26. Significant Figures -- Rounding And what would 763.48 cm be rounded to just one significant figure? To answer this question, let’s look at just the first significant figure: 763.48 cm. The “7” is followed by a “6”, so the “7” rounds up to an “8.” But the answer is obviously not 8 cm. Can you figure out what it should be? It should be 800 cm. This time two “0’s” are needed as place-keepers to keep the “8” in the hundred’s place.

27. Significant Figures -- Rounding Now, try rounding 3.8719 g off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper.

28. Significant Figures -- Rounding Now, try rounding 3.8719 g off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper. If you are finished, then continue.

29. Significant Figures -- Rounding Now, try rounding 3.8719 g off to… …four significant figures: 3.872 g …three significant figures: 3.87 g …two significant figures: 3.9 g …one significant figure: 4 g Were these the answers you got?

30. Significant Figures -- Rounding Now, try rounding 3.8719 g off to… …four significant figures: 3.872 g …three significant figures: 3.87 g …two significant figures: 3.9 g …one significant figure: 4 g Were these the answers you got? If not, try to figure out where you went wrong.

31. Significant Figures -- Rounding Now, try rounding 3.8719 g off to… …four significant figures: 3.872 g …three significant figures: 3.87 g …two significant figures: 3.9 g …one significant figure: 4 g Notice how this time we did not need to add any place-keeping “0’s” to any of the answers.

32. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper.

33. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper. If you are finished, then continue.

34. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: 6.984 L …three significant figures: 6.98 L …two significant figures: 7.0 L …one significant figure: 7 L Were these the answers you got?

35. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: 6.984 L …three significant figures: 6.98 L …two significant figures: 7.0 L …one significant figure: 7 L Were these the answers you got? If not, try to figure out where you went wrong.

36. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: 6.984 L …three significant figures: 6.98 L …two significant figures: 7.0 L …one significant figure: 7 L Notice that when the “9” rounded up in 6.9837 L, it becomes a “10.” The “0” goes where the “9” was and the “1” carries over to make the “6” turn into a “7:” 7.0 L

37. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: 6.984 L …three significant figures: 6.98 L …two significant figures: 7.0 L …one significant figure: 7 L And again, we didn’t need any place-keeping “0’s” in any of our answers.

38. Significant Figures -- Rounding Now, try rounding 6.9837 L off to… …four significant figures: 6.984 L …three significant figures: 6.98 L …two significant figures: 7.0 L …one significant figure: 7 L And again, we didn’t need any place-keeping “0’s” in any of our answers. (Remember: the “0” in “7.0 L” counts as a significant figure, not a place-keeper.)

39. Significant Figures -- Rounding Try rounding 54.298 s off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper.

40. Significant Figures -- Rounding Try rounding 54.298 s off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper. If you are finished, then continue.

41. Significant Figures -- Rounding Try rounding 54.298 s off to… …four significant figures: 54.30 s …three significant figures: 54.3 s …two significant figures: 54 s …one significant figure: 50 s Were these the answers you got?

42. Significant Figures -- Rounding Try rounding 54.298 s off to… …four significant figures: 54.30 s …three significant figures: 54.3 s …two significant figures: 54 s …one significant figure: 50 s Were these the answers you got? If not, try to figure out where you went wrong.

43. Significant Figures -- Rounding Try rounding 54.298 s off to… …four significant figures: 54.30 s …three significant figures: 54.3 s …two significant figures: 54 s …one significant figure: 50 s Here the only time we needed a place-keeping “0” was for the last answer (50 s) to keep the “5” in the ten’s place.

44. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper.

45. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: …three significant figures: …two significant figures: …one significant figure: Write your four answers out on a piece of paper. If you are finished, then continue.

46. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: 0.08148 km …three significant figures: 0.0815 km …two significant figures: 0.081 km …one significant figure: 0.08 km Were these the answers you got?

47. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: 0.08148 km …three significant figures: 0.0815 km …two significant figures: 0.081 km …one significant figure: 0.08 km Were these the answers you got? If not, try to figure out where you went wrong.

48. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: 0.08148 km …three significant figures: 0.0815 km …two significant figures: 0.081 km …one significant figure: 0.08 km Recall that the “0’s” at the beginning of a number (0.081479 km) are always place-keepers (never significant).

49. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: 0.08148 km …three significant figures: 0.0815 km …two significant figures: 0.081 km …one significant figure: 0.08 km So those beginning “0’s” must stay there in all the answers to keep all the significant figures in their correct places.

50. Significant Figures -- Rounding Try rounding 0.081479 km off to… …four significant figures: 0.08148 km …three significant figures: 0.0815 km …two significant figures: 0.081 km …one significant figure: 0.08 km So those beginning “0’s” must stay there in all the answers to keep all the significant figures in their correct places. No place-keeping “0’s” are needed at the end in any of the answers.