Download 02.03b Significant Figures

Chemistry 330
Name:
§ 02.03b
Date:
KEY
Significant Figures
Most Important Idea:
Background
Your measurements are only as good as the instrument you use. And in chemistry, the
measurements all relate to real, physical objects. As you recall, significant figures
indicate which digits in a measurement are meaningful. Significant figures are those
measured precisely plus one estimated digit. For example, in the value 10.003 g, the
10.00 are measured precisely; the 3, is estimated.

Preparation
Before coming to class do EITHER:
a) Watch and understand the following four videos on significant figures by the Khan
Academy:
1. Introduction: http://www.youtube.com/watch?v=eCJ76hz7jPM
2. Determining the rules: http://www.youtube.com/watch?v=eMl2z3ezlrQ
3. Addition & Subtraction: http://www.youtube.com/watch?v=xHgPtFUbAeU
4. Multiplication & Division: http://www.youtube.com/watch?v=iorZdz4dsBU
b) Read the textbook.
Rules for determining significant figures
Rule
1. Zeros appearing between non-zero numbers
are significant.
2. Zeros appearing in front of all non-zero digits
are not significant.
3. Zeros at the end of a number and to the right
of a decimal point are significant.
4. Zeros at the end of a number but to the left of
a decimal point:
a. If a zero has not been measured or estimated
but is just a placeholder, it is not significant.
b. A decimal place after the zeros indicates that
they are significant.
Examples
a. 40.7 L has 3 sig figs
b. 87,009 km has 5 sig figs
a. 0.095 897 m has 5 sig figs
b. 0.000 000 009 cg has 1 sig fig
a. 85.00 g has 4 sig figs
b. 9.000 000 000 mm has 10 sig figs
a. 2000 m has 1 sig fig
1700 L has 2 sig figs
b. 2000. m has 4 sig figs
1,000,000 has 1 sig fig
( 1,000,000. has 7 sig figs)
Example. How many significant figures are in each of the following?
28.6 g = 3 sig figs
3440.00 = 6 sig figs
F:\2014-2015\330_ModChem\330_sections\330_02_Measurements_and_Calculations\330.02.03b.Significant Figures HW-1_KEY.docx (9/16/2014)
Chemistry
330.02.03b_ Significant Figures
p. 2
Rounding
Numbers round up or down as you’ve learned from math classes. However, when the
number ends in 5 (e.g., 10.5) you don’t always round up. This would skew a series of
measurements always up. So, in science, we round to the even number to achieve a
more representative mean.
Example. Round the following to two digits: 10.5 L  10. L (round to even);
11.5 L  12 L
Adding & Subtracting 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 place.
Example.
7,000,000 year
25.1 g
+
101 year
+ 2.03 g
7,000,000 year
27.1 g
Multiplying & Dividing with Significant Figures
When adding or subtracting decimals, the answer must have the no more significant
figures than the measurement with the fewest number of significant figures. Density;
3.05 g / 8.47 mL = 0.360094451 g/mL. But the number with the fewest number of
significant figures is 3.05 (3 s.f.), so the answer is 0.360 g/mL.
Example. (3.0567 g) / (8.47 mL) = 0.36088548 g/mL without the correct number of
significant figures. However, 8.47 has the fewer number of sig figs (3), so the answer
has the same number of sig figs: (3.0567 g) / (8.47 mL) = 0.361 g/mL
Problems
Significant Figures
1. How many significant figures in each of these measured quantities?
(a) 4867 miles
(b) 56 mL
(c) 60,104 tons
4
2
5
2. How many significant figures are in the following?
(a) 40.2 g/cm3
(b) 0.0000003 cm
(c) 70 min
3
1
1
Round the following numbers as indicated:
3. To four figures.
(a) 3.682417
(b) 21.860051
(c) 375.6523
3.682
21.86
375.7
4. To one decimal place:
(a) 1.3511
(b) 2.473
1
2
(c) 5.50
6
(d) 2900 g.
2
(d) 4.6 × 1019 atoms.
2
(d) 112.511
112.5
(e) 45.4673
45.47
(d) 7.555
8
(e) 8.235
8
Chemistry
330.02.03b_ Significant Figures
5. To two decimal places:
(a) 22.494 (b) 79.2588
22.49
79.26
(c) 0.03062
0.03
p. 3
(d) 3.4125
3.41
(e) 41.8663
41.87