Download Tutorial 2 - Significant figures

SCHOOL OF PHYSICS AND CHEMISTRY – CHEM 181 - HOWARD COLLEGE – 2013
Tutorial # 2
Scientific notation, Significant figures and Handling numbers from measurements
1. Uncertainty and Scientific Notation
The uncertainty associated with a measurement whose value is expressed in scientific notation
cannot be obtained directly from the coefficient in the scientific notation. The coefficient
decimal point located is not the true location for the decimal point.
The value of the exponential term must be taken into account in determining uncertainty.
Determining Uncertainty:
Calculate the uncertainty for the number 3.753 x 102
10-3 (uncertainty in coefficient) x 102 (exponential term) = 10-1 (uncertainty in value)
The uncertainty in the number 3.753 x 102 is 10-1 (±0.1) ( in the tenth’s place)
Therefore the number can be rewritten in decimal place to show the uncertainty, that is:
3.753 x 102 = 375.3
Practice Exercise:
Calculate the uncertainty of the following numbers and rewrite in decimal form to show this
uncertainty.
a) 4.200 x 104
b) 4.2 x 105
c) 4.2 x 10-1
d) 4.200 x 10-3
Answers:
Uncertainty
a) ±10
b) ±10 000
c) ±0.01
d) ±0.000001
SCHOOL OF PHYSICS AND CHEMISTRY – CHEM 181 - HOWARD COLLEGE – 2013
2.
3.
Determine the number of significant figures in each of the following numbers:
a) 0.43571
b) 0.00621
e) 3300
f) 3300.00
c) 0.505023
d) 0.0000003
Round off the following measured chemical values to:
four significant figures:
a) 233.3723
b) 33.3723
c) 6.3723
d) 1.03723
c) 67.45
d) 67.35
c) 0.200007
d) 0.356303
three significant figures:
a) 42 303
b) 42 360
two significant figures:
a) 0.000333
4.
b) 0.01234
Carry out the following multiplications and divisions, and express your answers to the
correct number of significant figures:
a) 4.2337 x 0.00706
b) 3700 x 37.00 c) 4.5 x 4.05 x 4.50 d) 0.100 x 0.001 x 0.010
e) 5671 ÷ 4.44
f) 5.01 ÷ 5.07
g) (1.171 x 106) x (2.555 x 102)
h) (4.500 x 1010) ÷ (5.0005 x 10-8)
5.
Calculate the following mathematical operations involving both multiplication and
division and express your answers to the correct number of significant figures:
a)
4.5 𝑥 6.3
7.22
b)
5.567 𝑥 3.0001
3.45
2.322 𝑥 4.00
c) 3.200 𝑥 6.73
5600 𝑥 300
d) 22 𝑥 97.1
SCHOOL OF PHYSICS AND CHEMISTRY – CHEM 181 - HOWARD COLLEGE – 2013
6.
Carry out the following addition and subtraction mathematical operations and express
your answers to the correct number of significant figures:
a) 12 + 23 + 127
b) 3.111 + 3.11 + 3.1
c) 0.06 + 1.32 + 7.901
d) 1237.6 + 23 + 0.12
e) 43.65 – 23.7
f) 4.72 – 3.908
g) 4.111 – 3.07
h) 3.12 – 0.00007
i) 3.245 x 103) + (1.1 x 103)
j) (9.870 x 10-2) – (5.7 x 10-3)
7.
Carry out the following operations involving both addition and subtraction and express
your answers to the correct number of significant figures:
a) 999.0 + 1.7 -43.7
8.
9
b) 345 – 6.7 + 4.33
c) 4.3 + 230 – 20 – 13.00
Calculations involving both significant figure rules:
a) 1.20 x (2.33 + 4.5)
b) 0.300 x (3.73 + 3.0 + 2.777)
c) 0.400 x (4.5 + 2.33)
d) 4.2 x 5.30 x (28 – 11)
e) 3.111 + 5.03 ÷ 100 x 33
f) 5.03 – 3.111 ÷ 100 + 33
What is the uncertainty, in terms of a power of ten, associated with each of the
following measured chemical values?
a) 3.700 x 104
b) 3.700 x 106
end of tutorial