1. Measurements:
Every measurement has UNITS.
Every measurement has UNCERTAINTY.

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.

3. Precision can also mean
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. 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

6. 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
Counted numbers and definitions (2.54 cm = 1 inch) are considered to be exact and have no effect on the number of sig. figs. reported in calculations with measurements.

7. 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.)

8. 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

9. Measurement Calculations with scientific notation.
Addition/subtraction: must be placed into the same notation.
(2.3 x 103) + (3.2 x 104) =
0.23 x 104
x 104
3.43 x 104
= 3.4 x 104

10. Calculations with Sig. figs.
Multiplication and division (measurements):
Count sig figs!!
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

11. Remember to follow the correct order of operations!!
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!!

12. 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
15.76 / 7.5 =
(count sig figs)
= 2.1

13. 1. The term that is related to the reproducibility (repeatability) of a measurement is
a. accuracy.
b. precision.
c. qualitative.
d. quantitative.
e. property.
Let’s take a “Quiz”
b. precision.
2. The number of significant figures in the mass measured as g is
a. 1.
b. 2.
c. 3.
d. 4.
e. 5.
e. 5.

14. 3. The number of significant figures in 6.0700 x 10-4… is
d. 6.
e. 7.
c. 5.
4. How many significant figures are there in the value ?
a. 7
b. 6
c. 5
d. 4
e. 3
d. 4

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

16. 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 %