1. SIGNIFICANT
FIGURES

2. What are Significant Figures?
The significant figures in a measurement
consist of all the digits known with certainty plus one final digit, which is uncertain or is estimated.

3. Your reading might be 76 ml
Your reading might be 76 ml. But, how sure are you that it is really 76 ml? Is it possible that it’s also or 76.01?
CERTAIN VALUE: 75
UNCERTAIN VALUE: 0.99~1.1

4. All measurements are approximations—no measuring device can give perfect measurements without experimental uncertainty. By convention, a mass measured to 13.2 g is said to have an absolute uncertainty of plus or minus 0.1 g and is said to have been measured to the nearest 0.1 g. In other words, we are somewhat uncertain about that last digit—it could be a "2"; then again, it could be a "1" or a "3". A mass of g indicates an absolute uncertainty of plus or minus 0.01 g.

5. Precision & Measurement
Measurements are always all measured values plus one
approximated value. The pencil is 3.6 cm long.
With more calibration a more
precise measurement is possible
The pencil is 3.64 cm long! 4
The calibration of the instrument
determines measurement precision
Now cm !

7. What is Accuracy?
Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.
►Who is more accurate when measuring a book that has a true length of 17.0cm?
Andrea:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

8. What is Precision?
Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.
►Who is more precise when measuring the same 17.0cm book?
Andrea:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

9. Rules For Significant Figures
Significant figures are used for measured numbers and for numbers derived from measurements; does not include
definitions (ex. 1000ml=1L) or
counting numbers (ex. 1,2,3 etc)
10 mm = 1cm = (2 significant figures)
100cm = 1m = (3 significant figures)
1000g = 1kg= (4 significant digits)

10. 2. Digits from 1-9 are always significant.
Ex = 4 significant figures
25 = 2 significant figures
23.42 = 4 significant figures

11. 3. Zeros between two other significant digits are always significant.
Ex g = 4 significant figures
207 ml = 3 significant figures

12. 4. One or more additional zeros to the right of both the decimal place and another significant digit are significant.
Ex = 3 significant figures
50.05 = 4 significant figures
50.50 = 4 significant figures

13. Ex. 0.007 (1 significant figure) 1000 ( 1 significant figure)
5. Zeros used solely for spacing the decimal point (placeholders) are not significant.
Ex (1 significant figure)
1000 ( 1 significant figure)
0.015 ( 2 significant figures)

14. 6. Exact numbers have an infinite number of significant digits but they are generally not reported. All non zero digits are significant.
Ex. 2 ( 1 significant figure)
453 (3 significant figures)

15. Significant Figures 1 yard = 3 feet 4 quarts = 1 gallon
Exact equivalences have an unlimited number of
significant figures
1 yard = 3 feet
There are exactly 3 feet in exactly 1 yard.
Therefore the 3 can be 3 or 3.0 or 3.00 or etc.
and the 1can be 1 or 1.0 or 1.00 or etc. !
The same is true for:
4 quarts = 1 gallon
100 centimeters = 1 meter
1000 grams = 1 kilograms
and so on !

16. SUMMARY EXAMPLES # OF SIG. FIG Rules 453 kg 3
All non-zero digits are always significant.
5057 L 4
Zeros between 2 sig. dig. are significant.
5.00 g
Additional zeros to the right of decimal and a sig. digits are significant.
0.007 ml 1
Placeholders are not sig. ml
Zeros to the right of the decimal and to the right of non zeros are significant.

17. How many significant figures do the following numbers have?
It’s Your Turn To Try!
How many significant figures do the following numbers have?

18. 1) 1234 _____
2) _____
3) 890 _____
4) _____
5) _____
6) _____
7) _____
8) _____
9) _____
10) 72 _____
11) 1000 _____
12) _____
13) _____
14) _____
15) 8120 _____
1.) 4
2.) 2
3.) 2
4.) 4
5.) 5
6.) 8
7.) 3
8.) 2
9.) 6
10.)2
11.) 1
12.) 6
13.) 1
14.) 3
15.) 3

19. ASSIGNMENT:
Determine the number of significant digits in the following numbers.
1) 5600 _____
2) 45.00_____
3) 105.0_____
4) _____
5) _____
6) _____
7) 5, 056, 300_____
8) _____
9) 93, 000, 000_____
10) 21.35_____

20. The End