1. Significant Digits or “Figures”
How to recognize significant figures when:
Taking a measurement
Reading a measurement
Performing a calculation

2. Accuracy and Precision in Measurements
Accuracy: how close a measurement is to the accepted value.
Precision: how close a series of measurements are to one another or how far out a measurement is taken.
A measurement can have high precision,
but not be as accurate as a less precise one.

3. Significant Figures are used to indicate the precision of a measured number or to express the precision of a calculation with measured numbers.
In any measurement
the digit farthest to the right is considered to be estimated. 1 2
2.0
1.3

4. Question For Thought
Using two different rulers, I measured the width of my hand to be 4.5 centimeters and centimeters. Explain the difference between these two measurements.

5. The first measurement implies that my hand is somewhere between 4
The first measurement implies that my hand is somewhere between 4.5 and 4.9 cm long. There is a uncertainty in this number because we have to estimate.
The second measurement implies that my hand is between 4.5 and 4.6 cm long. This measurement is more certain due to its greater precision.

6. More certain due to greater precision
4.5 cm
2 significant figures
Uncertain
4.54 cm
3 significant figures
More certain due to greater precision
Significant figures are necessary to reduce
uncertainty in our measurements.
Significant figures indicate the precision of the measured value!!

7. Significant Figures
Scientist use significant figures to determine how precise a measurement is
Significant digits in a measurement include all of the known digits plus one estimated digit
So when reading an instrument…
Read instrument to the last digit that you know
Estimate or “eyeball” the final digit

8. For example… Look at the ruler below Each line is 0.1cm
You can read that the arrow is on 13.3 cm
However, using significant figures, you must estimate the next digit
That would give you cm

9. Let’s try this one Look at the ruler below
What can you read before you estimate?
12.8 cm
Now estimate the next digit…
12.85 cm

10. Let’s try graduated cylinders
Look at the graduated cylinder
What can you read with confidence? = 56 ml
Now estimate the last digit = 56.0 ml
What is this measurement?
_____________

11. Recognizing # Sig Figs in a Number
All non zero digits are ALWAYS significant
How many significant digits are in the following numbers?
______Significant Figures
______Significant Digits
274
25.632
8.987

12. All zeros between significant digits are ALWAYS significant
How many significant digits are in the following numbers?
504
60002
9.077
________ Significant Figures
________ Significant Digits

13. All FINAL zeros to the right of the decimal ARE significant
How many significant digits are in the following numbers?
______Significant Figures
______Significant Digits
32.0
19.000

14. _____Significant Digit _____Significant Digits
All zeros that act as place holders are NOT significant Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal
How many significant digits are in the following numbers?
_____Significant Digit _____Significant Digits x

15. Numbers with no decimal are ambiguous...
Does 5000 ml mean exactly 5000?
Maybe.... Maybe Not!
So 5000, 500, 50, and 5 are all assumed to have 1 significant figure
If a writer means exactly 5000, he/she
must write or x 103

16. All counting numbers and constants have an infinite number of significant digits
For example:
1 hour = 60 minutes
12 inches = 1 foot
24 hours = 1 day

17. How many significant digits are in the following numbers?
_______________ x

18. Here is a one sentence rule for counting sig figs:
All digits ARE significant except
Zeros preceding a decimal fraction
(ex: )
and
Zeros at the end of a number
containing NO decimal point
(ex: 45,000)

19. Calculations with Sig Figs
Adding or subtracting:
answer can have no more places after the decimal than the LEAST of the measured numbers.
Count # decimal places held
(nearest .1? .01? .001?)
Answer can be no more accurate than the LEAST accurate number that was used to calculate it.

20. 5.50 grams For Example: + 8.6 grams - 49.7 ml -------- -------------
2.39 ml --> 2.4 ml

21. Calculations with Sig Figs
Multiplying or dividing: round result to least # of sig figs present in the factors
Answer can’t have more significant figures than the least reliable measurement.
COUNT significant figures in the factors

22. 56.78 cm x 2.45cm = cm2
Round to 3 sig figs = 139cm2
75.8cm x 9.6cm = ?

23. Now let’s do some math..... (round answers to correct sig figs!)
g g
answer: 6.55 g
Did you need to count sig figs? NO!

24. Try this one.... 4.80 ml - .0015 ml answer: 4.80 ml
(one might say .0015
is insignificant
COMPARED TO 4.80)

25. Now try these... 5.0033 g / 5.0 ml answer: 1.0 g/ml
Did you have to count sig figs?
YES!

26. Here’s a tougher one..... 3.0 C/s x 60 s/min x 60 min/hr =
answer: C/hr rounds to C/hr
Note:
Standard conversion factors never limit sig. figures- instruments and equipment do.

27. Scientific Notation
Scientific notation is used to express very large or very small numbers
It consists of a number between 1 & 10 followed by x 10 to an exponent
Exponent can be determined by the number of decimal places you have to move to get only 1 number in front of the decimal

28. Large Numbers
If the number you start with is greater than 1, the exponent will be positive
Write the number in scientific notation
First move the decimal until 1 number is in front
Now add x 10
Now count the number of decimal places you moved (4)
Since the number you started with was greater than 1, the exponent will be positive
x 10 4

29. Small Numbers
If the number you start with is less than 1, the exponent will be negative
Write the number in scientific notation
First move the decimal until 1 number is in front = 5.2
Now add x 10
Now count the number of decimal places moved (3)
Since the number you started with was less than 1, the exponent will be negative
5.2 x 10 -3

30. Scientific Notation Examples
Place the following numbers in scientific notation
Note: all sig figs from the original number must be present!
______________

31. Going to Ordinary Notation Examples
Place the following numbers in ordinary notation:
________________
3 x x x x x 103