1. Significant Figures
(How Exact is Exact ?)

2. Part 1: significant figures and Certainty

3. The type of ruler used DOES make a difference !
As you saw from our short activity, the graduations on the measuring instrument used affects the certainty of our measurement
When you used the ruler with a scale of 0.1, your measurement was much more accurate than when you were using the ruler that was scaled by 10

4. The system of significant figures was devised so we can determine how reliable a measurement was.
Definition Significant Figures refers to those digits in a number that are directly read in a measurement plus one uncertain digit

5. REMEMBER If the reading is 23.57 cm, this means
Whenever you make any measurement, always include all the digits that you can directly read PLUS one uncertain digit.
REMEMBER
If the reading is cm, this means
that 2,3 and 5 are read directly on the
ruler, while 7 is estimated.
The number has four significant figures.

6. Part 2 : Counting Significant Figures
One easy method of finding the number of significant figures
in a number is through the
Pacific-Atlantic Rule

7. Pacific Rule P stands for the PRESENCE of a decimal point
P also stands for PACIFIC
Use this rule when you see that a number has a decimal point (decimal pt. is PRESENT)
RULE: If a number has a decimal point, count all digits (including zero) from the first nonzero digit at the LEFT

8. Think OF How THE Pacific Ocean HITS THE US COAST…
From LEFT

9. Examples Answer: 5 sig. figures Answer: 4 sig. figures
Count from first nonzero
digit at left (4) to the last digit at right (6)
Answer: 5 sig. figures 1) 2)
Count from first nonzero
digit at left (5) to the last
digit at right (0)
Answer: 4 sig. figures

10. Your Turn !! Find the no. of significant figures in: (1) 57,376. 205
(1) 57,
Answer: 8 sig. figs.
(2) 4,
Answer: 7 sig. figs.

11. More Questions…
(3)
1 2 3
Answer: 3 sig. figs.
(4)
Answer: 5 sig. figs

12. Atlantic Rule A stands for the ABSENCE of a decimal point
A also stands for ATLANTIC
Use this rule when the number has no decimal point ( decimal point is ABSENT)
RULE : If a number has no decimal point, count all digits starting from the first nonzero digit at the RIGHT

13. THINK OF HOW THE ATLANTIC OCEAN HITS THE US COAST…
From RIGHT

14. Examples Count from first nonzero
digit at right (9) to the leftmost digit (8)
Answer: 3 significant. figures
1) 879,
Count from first nonzero
digit starting at right (3) to the
leftmost digit (7)
Answer: 4 significant figures
762,300

15. NUMBERS IN SCIENTIFIC NOTATION
How many significant figures are there in
6.02 x 1023
RULE:
For numbers in scientific notation, all the numbers in the decimal part are significant…
ANSWER: 3 significant figures

16. How many significant figures are there in each of these numbers?
1) 3300 2) 3) 4)
5) 0.90
6) X 106 7) 8)

17. Check your answers: Now, wasn’t that easy!!! 1) 2 2) 3 3) 5 4) 4 5) 2
6) 3
7) 5
8) 2
Now, wasn’t that easy!!!

18. PART 3: ROUNDING OFF
Let’s Review !

19. Don’t lose it… The number of significant figures
in a measurement indicates the
reliability of that measure
When you do a mathematical operation (add, subtract, multiply….) on that number be sure to ROUND OFF properly so the answer reflects the reliability of the original measurement

20. Say what?
ROUND OFF !!!
One skill you learned in grade school is how to round off a number
Can you still remember how you
solved such problems…

21. PROBLEM: Round off the number 64.0384 to the underlined place
RULE: If the number following the underlined decimal place is 5 or greater than 5 , add 1 to the underlined digit. Drop all the numbers after it.
SOLUTION:
You must round up to 3
The digit following 3 is 8
8 is greater than 5, so add 1 to 3 and
the underlined digit becomes 4
Drop all numbers after 4
ANSWER:

22. PROBLEM: Round off the number 8.3722 to the underlined place
RULE : If the number following the underlined decimal place is less than 5, keep the underlined digit. Drop all the numbers after it.
SOLUTION:
You must round up to 7
The digit following 7 is 2
2 is less than 5 so keep the underlined digit (7)
Drop all the numbers after
ANSWER: 8.37

23. Now it’s YOUR turn! Round each number to the underlined digit:
(1)
Think …must round up to 4
… 4 is followed by 2
Since 2 is less than 5,
…must keep 4
Drop numbers after 4
Answer:

24. Next number (2) 7.2619 Think …must round up to 2 … 2 is followed by 6
(2)
Think …must round up to 2
… 2 is followed by 6
Since 6 is greater than 5,
…must add 1 to 2
So 2 becomes 3
Drop all numbers after 3
Answer: 7.3

25. And one more… (3) 8234.67 Think …must round up to 2
(3)
Think …must round up to 2
… 2 is followed by 3
Since 3 is less than 5,
…must keep 2
Drop all numbers after 2,
but to indicate place value
keep two zeros
Answer:

26. Don’t forget to connect ROUNDING OFF with SIGNIFICANT FIGURES
Problem 1:
Round off to three significant
figures
A decimal point is Present, so follow Pacific rule
(count from the first nonzero digit at the left)
You must round up to 1 ( )
ANSWER: 56.2

27. Problem 2: Round off 0.006392 to two significant figures
A decimal point is Present, so follow Pacific rule
(count from the first nonzero digit at the left)
You must round up to ( )
ANSWER:

28. Practice Problems:
Round these measurements to three significant figures:
kg. m cm
256,769 mg m
405,670,000 mL

29. Did you get these answers?
kg. m
457 cm
257,000 mg
5.93 m
406,000,000 mL

30. CALCULATIONS INVOLVING SIGNIFICANT FIGURES
PART 4
CALCULATIONS INVOLVING SIGNIFICANT FIGURES

31. MULTIPLICATION and DIVISION
RULE:
Round off the answer so that it has the same number of significant figures as the measurement with the fewest significant figures
5.3 x x =
(2 sf) (3 sf) (3 sf)
You must round off so that
it has 2 sig. figures .
ANSWER: 26

32. Now give these questions a try:
8.2 cm x cm =
4,170 m2 ÷ m =
9.3 mm x mm x mm =

33. Did you get the right answers?
(1) becomes 52
Answer: 52 cm2
(2) 834 becomes 830
Answer: 830 m
(3) becomes 47
Answer: 47 mm3

34. ADDITION AND SUBTRACTION
RULE:
Round off the answer so that it has the same number of decimal places as the measurement with the least number of
decimal places.
(one decimal place)
(one decimal place)
(two decimal places)
32 .86
Round off the answer to one decimal place
ANSWER: 32.9

35. How about these problems?
Find the sum of cm cm cm
Problem 2: Get the difference of m m

36. So how well did you do? Problem 1: 6.730 cm (3 decimal places)
Answer must be rounded off to 1 decimal place
Answer: cm

37. Problem 2: 68.731 m (3 decimal places) - 14.22 m (2 decimal place)
Answer must be rounded off
to 2 decimal places
Answer: m

38. So good luck on sig figs and let’s keep trying !!!