1. GHS Enriched Chemistry Chapter 2, Section 3
Accuracy versus Precision
Accuracy
Accuracy is how close a measured value is to the actual (true) value.
Precision
Precision is how close the measured values are to each other.
the degree of exactness of a measurement – depends on the measuring instrument

2. Accuracy and Precision (reference page

3. Percentage Error
Percentage error shows how close your results are compared to the accepted value.
It’s a way of showing how well you completed a lab.
Complete practice problems 1 and 2 on page 43

4. Percentage Error – Practice Problems page 43
1. 2.

5. Error in Measurement
Some error or uncertainty always exists in any measurement.
Can be caused by human error or the measuring device
When we make a measurement, we record all known digits and estimate one digit.

6. The measuring device determines how you record your measurements!

7. Significant Figures
Significant figures in a measurement consist of all the digits known with certainty plus one estimated digit.
Significant figures are critical when reporting data b/c they give the reader an idea of how precise your data is.
We don’t worry about significant figures when using “exact” numbers, because they are known with complete certainty.

8. Why are significant figures important
Why are significant figures important? Complete the following density problem:
A cube has a volume of 23.5 cm3 and a mass of 18.2 grams. Calculate the density.
The calculated answer is g/cm3
Clearly, we cannot express our answer to the tenth decimal place. So how do we round? That’s where sig figs become important!

9. (These can all be found on page 45 of your text.)
Rules for determining significant figures in a measurement.
(These can all be found on page 45 of your text.)
All nonzero digits are significant:
1.234 g has 4 significant figures
(2) Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures

10. (These can all be found on page 45 of your text.)
Rules for determining significant figures in a measurement.
(These can all be found on page 45 of your text.)
(3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point:
0.001 oC has only 1 significant figure
(4) Trailing zeroes that are also to the right of a decimal point in a number are significant:
mL has 3 significant figures

11. (5) Zeros at the end of a number but to the left of a decimal point may or may not be significant.
190 miles may be 2 or 3 significant figures, 50,600 calories may be 3, 4, or 5 significant figures.
50,600. contains 5 sig figs because of the decimal point.

12. We can also use scientific notation to indicate the number of sig figs.
- the number of significant figures is indicated by the number of numerical figures in the 'digit' term.
For example, depending on whether the number of significant figures is 3, 4, or 5, we would write 50,600 calories as:
5.06 × 104 (3 significant figures) × 104 (4 significant figures), or × 104 (5 significant figures).

13. Significant Figures
How many significant figures are in each of the following measurements?
a g
b cm
c. 910 m
d L
e kg
f x 104 g
g mg

14. Lets try some more. How many significant figures are there in the following measurements:
45.0 cm ______
km ______
.0045 m ______
1.020 g ______
6500. m ______
4.00 L ______
.0025 km ______
g ______

15. Rounding Numbers
Sometimes when we perform calculations using measurements, we end up with an answer that has more numbers than we can have
When this occurs, we need to round to the required number of sig figs.
There are rules that we must follow when rounding numbers.
For example, suppose we have to round the following calculations to 3 sig figs:
3.627 cm =
3.621 cm =
cm =
3.625 cm =
3.675 cm =
3.63 cm =
3.62 cm =
3.68 cm =

16. Rounding
When we need to drop digits and round, there are set rules we need to follow:

17. Significant Figures + Addition or Subtraction with Significant Figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
Example: cm cm +

18. Now you try a couple! g g
km km _ +

19. Multiplication or Division with Significant Figures
For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.
Examples:
3.2 cm x 1.20 cm =
120.4 g / 3.2 cm3 =
3.84 cm2
g/cm3
= 3.8 cm2
= 38 g/cm3

20. a. 5.44 m + 2.6103 m = b. 2.4 m  15.82 m = Sample Problem
Significant Figures
Sample Problem
Carry out the following calculations. Express each answer to the correct number of significant figures.
a m m =
b m  m =

21. Let’s try a couple practice problems.
= ?
= ?
4.56 x 2.5 = ?

22. Math using sig figs
Practice Problems

23. Addition/Subtraction
cm m
cm m
g km
g km

24. Multiplication/Division
34.5 m x 1.2 m =
1,200 kg x 2.3 kg =
34.6 m / 4.2 =
.3400 g / 8.2

25. Rounding 43.48 cm (to 3 sig figs) = 12.42 cm (to 3 sig figs) =
9.275 g (to 3 sig figs) =
20.35 g (to 3 sig figs) =

26. Try these problems:
72.49 in 3 sig. fig. is ___________
in 2 sig. fig. is ___________
45.52 in 3 sig. fig. is ___________
92,528 in 4 sig. fig. is ___________
in 4 sig. fig. is ___________
13,052 in 3 sig. fig. is ___________
239.5 in 3 sig. fig. is ___________
2.448 x 104 in 3 sig. fig. is ___________
in 3 sig. fig. is ___________
in 3 sig. fig. is ___________
63500 in 2 sig. fig. is ___________
89999 in 3 sig. fig. is ___________