1. Measurement and Significant Figures

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

3. Measurement Precision can also mean Ex.
The number of decimal places assigned to the measured number (The more decimal places, the more precise the measurement)
Ex.
2.1 cm
2.10 cm
2.100 cm

4. the digit farthest to the right is considered to be estimated.
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

5. Significant Figures in Measurement
Every experimental measurement has a degree of uncertainty.
The volume at the right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.

6. What is the length of the wooden stick?
Practice
What is the length of the wooden stick?
1) cm
2) cm
3) cm

7. Measured Numbers
Do you see why Measured Numbers have error…you have to make that Guess!
All but one of the significant figures are known with certainty.
The last significant figure is only the best possible estimate.

8. Sig. Fig. Rules (with measurements):
1. All non-zero digits are significant.
3 sig figs
sig figs
sig figs
2. Zeros that come before the first non-zero digit are NOT significant
sig fig
sig figs
sig figs

9. 3. Zeros in between two significant figures ARE significant
sig figs
sig figs
4. Final zeros after a decimal point are significant
sig figs
sig figs
sig figs
sig figs
sig figs
sig figs

10. How many sig figs are there in each of the following measurements?
1.)
7.)
2.)
8.)
3.) 100.3
9.)
4.) 0.678
10.)
5.) 1.008
11.)
6.)
12.)

11. Sig Fig rules DO NOT apply to Exact Numbers!!!
An exact number is a counting number or an exact conversion.
1. Counting objects are always exact 2 soccer balls 4 pizzas
2. Exact conversions are predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm
Sig Fig rules DO NOT apply to Exact Numbers!!!

12. significant to the 0.1 place
Calculations with Sig. Figs.
Addition and Subtraction:
Look at decimal places! Answer should have the same amount of decimal places as the measurement with the least amount cm cm cm cm
= cm
significant to the 0.1 place

13. Calculations with Sig. Figs.
Multiplication and Division:
Count sig figs!!
Your answer should have the same amount of sig figs as the measurement with the least amount.
2.734 cm x 5.2 cm x cm =
cm3
4 s.f.
2 s.f.
5 s.f.
written as 120 cm3
2 s.f.’s

14. When both addition/subtraction and multiplication/division appear in the same problem
Since the rules are different for each type of operation, when they both occur in the same problem,
complete the first operation and establish the correct number of significant digits.
Then proceed with the second operation and set the final answer according to the correct number of significant digits based on that operation
Remember to follow the correct order of operations!!

15. First Add: 1.245 + 6.34 + 8.179 = = 15.76 Then divide by 7.5
(count decimal places)
= 15.76
Then divide by 7.5
5.76 / 7.5 =
(count sig figs)
= 2.1

16. Percent Error your value accepted value
Indicates accuracy of a measurement
your value
accepted value

17. Percent Error % error = 2.9 %
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
% error = 2.9 %