Transcript Chapter 1 Section 3: Measurements and Calculations in

Objectives:
(1)To determine the number of
significant figures in a
measurement.
(2) To perform calculations using
significant figures.
Chapter 1
Section 3: Measurements and
Calculations in Chemistry
Accuracy and Precision
• Accuracy is a description of how close a
measurement is to the true value of the
quantity measured.
• Precision is the exactness of a measurement.
Accuracy and Precision
NEITHER PRECISE NOR ACCURATE
BOTH PRECISE AND ACCURATE
PRECISE BUT NOT ACCURATE
Significant Figures (sig figs)
• Sig Figs tell us how good the data we are using
are.
Rules for Determining Sig Figs
1. All non-zero digits are significant.
123 = 3 sig figs
8,476 = 4 sig figs
934,526 = 6 sig figs
2. All zeros, between non-zero digits, are
significant.
101 = 3 sig figs
2,000,503 = 7 sig figs
3,009 = 4 sig figs
3. Reading left to right, all ending zeros, without
a decimal point, are not significant.
6,000 = 1 sig fig
120 = 2 sig figs
407,000 = 3 sig figs
4. Reading left to right, all ending zeros, with a
decimal point, are significant.
400. = 3 sig figs
122.000 = 6 sig figs
5,020.0 = 5 sig figs
5. Reading left to right, all starting zeros after a
decimal point are not significant.
0.0012 = 2 sig figs
0.0609 = 3 sig figs
0.000000003 = 1 sig fig
How Many Sig Figs?
a.
b.
c.
d.
e.
f.
25 cm
305 cm
0.00123 in
400 g
400. m
0.94600 mL
How Many Sig Figs?
a.
b.
c.
d.
e.
f.
25 cm = 2
305 cm = 3
0.00123 in = 3
400 g = 1
400. m = 3
0.94600 mL = 5
Answers
a.) 5,490,000 m
b.) 0.0134793 mL
c.) 31,950 cm2
d.) 192.67 m2
e.) 790 cm
f.) 389,278,000 J
Calculations with Sig Figs:
Addition and Subtraction
Your answer can only be as accurate as the least accurate
measurement used in the calculation.
1. Complete the calculation.
2. Determine the number of digits to the right of the
decimal point in each measurement used in the
calculations.
3. Round answer so that it has that same number of
digits to the right of the decimal as the measurement
with the smallest number of digits to the right of the
decimal.
Example: 3.95 g + 2.87 g + 213.6 g
Example
3.95 g + 2.87 g + 213.6 g = 220.42 g
3.95 g has 2 numbers after the decimal
2.87 g has 2 numbers after the decimal point
213.6 g has 1 number after the decimal point
Therefore, the answer must have 1 number after the
decimal point.
Answer = 220.4 g
Example
Solve: 4.999 mL – 1.2 mL
4.999 mL – 1.2 mL = 3.799 mL
4.999 mL has 3 numbers after the decimal
1.2 mL has 1 number after the decimal
Therefore, the answer must have 1 number after the
decimal.
Answer = 3.8 mL
Practice
1.) 0.1273 mL – 0.008 mL
2.) 1.222 cm + 3.55 cm + 1.0 cm
3.) 3.2 g – 1.4 g + 0.33 g
4.) 34.09 L – 1.230 L
5.) 32.89 g + 14.21 g
Answers
DON’T FORGET UNITS!
1.) 0.1273 mL – 0.008 mL = 0.1193 mL  0.119 mL
2.) 1.222 cm + 3.55 cm + 1.0 cm = 5.772 cm  5.8 cm
3.) 3.2 g – 1.4 g + 0.33 g = 2.13 g  2.1 g
4.) 34.09 L – 1.230 L = 32.860 L  32.86 L
5.) 32.89 g + 14.21 g = 47.1 g  47.10 g
Calculations with Sig Figs
Multiplication and Division
Your answer can only be as accurate as the least
accurate measurement used in the calculation.
1. Complete the calculation.
2. Determine the number of sig figs in each
measurement used in the calculations.
3. Round answer to the same number of sig figs as
the least accurate measurement.
Example: 651 cm x 75 cm
Example
Solve: 651 cm x 75 cm
651 cm x 75 cm = 48825 cm2
651 cm has 3 sig figs
75 cm has 2 sig figs
Therefore, the answer must have 2 sig figs.
Answer = 49000 cm2
Practice
Perform the following calculations and express
the answer in the correct units and number of
sig figs.
1.) 7.835 kg / 2.5 L
2.) 14.75 L / 1.20 s
3.) 360 cm x 51 cm x 9.07 cm
4.) 5.18 m x 0.77 m x 10.22 m
5.) 34.95 g / 11.169 cm3
Answers
Perform the following calculations and express
the answer in the correct units and number of
sig figs.
1.) 7.835 kg / 2.5 L = 3.1 kg/L
2.) 14.75 L / 1.20 s = 12.34 s
3.) 360 cm x 51 cm x 9.07 cm = 170,000 cm3
4.) 5.18 m x 0.77 m x 10.22 m = 41 m3
5.) 34.95 g / 11.169 cm3 = 3.129 g/cm3
Practice
1.) (12.4 cm x 7.943 cm) + 0.0064 cm2
2.) (246.83 g/26) – 1.349 g
Answer
1.) (12.4 cm x 7.943 cm) + 0.0064 cm2
First multiply and second add.
12.4 cm x 7.943 cm = 98.4932  98.5 cm2
98.5 cm2 + 0.0064 cm2 = 98.50064 cm2  98.5 cm2
2.) (246.83 g/26) – 1.349 g
First divide and second subtract.
246.83 g/26 = 9.4934615 g  9.5 g
9.5 g – 1.349 g = 8.151 g  8.2 g
A rectangle measures 87.59 cm by 35.1 mm.
Express its area with the proper number of sig
figs in the specified unit:
in cm2
in mm2
in m2
Answer
A rectangle measures 87.59 cm by 35.1 mm. Express
its area with the proper number of sig figs in the
specified unit:
in cm2 : 87.59 cm x 3.51 cm = 307 cm2
in mm2 : 875.8 mm x 35.1 mm = 30700 mm2
in m2 : 0.8759 m x 0.0351 m = 0.0307 m2