This document discusses the rules for determining significant digits in measurements and calculations. It defines four main rules:
1. All non-zero digits are significant, as are zeros between non-zero digits.
2. Leading zeros are not significant.
3. Trailing zeros may or may not be significant, depending on whether a decimal is present.
4. In calculations, the answer should match the least number of significant digits in the input values.
It provides examples like 0.08006 having 4 significant digits, and 1000mL having 1 significant digit. The document also covers rounding rules and calculating volumes and perimeters based on measurements to the correct number of significant digits.
Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors
Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors
Identify the place value up to thousands
Express the numbers into words with place value
Express the number into expanded form by addition
Express the number into expanded form by multiplication
Identify the place value up to thousands
Express the numbers into words with place value
Express the number into expanded form by addition
Express the number into expanded form by multiplication
significant figures (measurements) lec 07 Sindh text book boardTalal Khan
Chapter02 Measurements (Significant Figures) Lec-07
Learning Objectives
Review
Introduction to significant figures
Rules of Significant figures
Practice Questions
Review Questions
Significant Figures
Only those figures or digits of a numerical quantity which are the result of actual measurement are said to be significant.
Rules of Significant Figures
Rule 01 All non zeros are significant figures Example. 3.14
Rule 2 Zeros Between non zeros are significant Example 1001
Home Task
Write the number of significant figures
(1, 400, 12002,100.0, 0.0001,10x104, 150.000, 17000,1200.010, 1222.00, 111, 000, 1.000)
Thank You For Your Cooperation
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5. SIGNIFICANT DIGITS
Rule #4:
Zeros that are located to the right of
a value may or may not be
significant
Ex. 1000.mL
4 significant digits
Ex. 1000mL
1 significant digit
7. SIGNIFICANT DIGITS
Ex. 1000.0mL 5 significant digits
Why?
Rule #5
Any 0’s to the right of a decimal that
are not followed by any number are
significant
8. CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #1: Multiplying and Dividing
1.008 x 4.67
= 4.70736
= 4.71
This value has the
lowest number of
significant digits
The value with the lowest number of significant
digits determines how many significant digits
will appear in the answer
9. CALCULATIONS WITH
SIGNIFICANT DIGITS
Rule #2: Adding and Subtracting
1.008 + 4.67
= 5.678
= 5.68
This value has the
lowest number of
decimal places
The value with the lowest number of decimal
places determines how many decimal places
will appear in the answer
15. SIGNIFICANT DIGITS
Practice: How many
significant digits are in
the following values?
a) 5.703
b) 70
c) 100.
d) 395830
e) 0.0101
f) 21.0
Practice: Round the
following numbers to 2
significant digits
a) 1.01
b) 24.5
c) 17.5
d) 25.6
e) 48665
f) 11.5
16. SIGNIFICANT DIGITS
Practice: Calculate the
perimeter of the
following shape
Practice: Calculate the
volume of the following
rectangular prism
2.67cm
2.562cm
1cm
1.5cm
2.8753cm
1.43cm
11.54cm
8.7cm
10.56cm
17. SIGNIFICANT DIGITS
Practice: How many
significant digits are in
the following values?
a) 5.703 4
b) 70 1
c) 100. 3
d) 395830 5
e) 0.0101 3
f) 21.0 3
Practice: Round the
following numbers to 2
significant digits
a) 1.01 1.0
b) 24.5 24
c) 17.5 18
d) 25.6 26
e) 48665 4.9x104
f) 11.5 12
18. SIGNIFICANT DIGITS
Practice: Calculate the
perimeter of the
following shape
Practice: Calculate the
volume of the following
rectangular prism
2.67cm
2.562cm
1cm
1.5cm
2.8753cm
1.43cm
11.54cm
8.7cm
10.56cm
= 12.0373cm
= 12cm
= 1060.20288cm3
= 1.1x103
cm3
19. SIGNIFICANT DIGITS
Significant digits for logarithmic values:
If a solution had an H+
concentration of 2.5x10-4
mol/L,
then what is the pH to the correct number of significant
digits?
i.e. pH = - log [2.5x10-4
mol/L]
pH = 3.602059
These two digits are significant
This digit is derived from the power of 10, so it is not a significant digit
The two digits to the right of the decimal are significant
.: pH = 3.60
20. SIGNIFICANT DIGITS
What is the volume of the graduated cylinder?
What digits are you absolutely sure about?
6.6mL, 6.61mL, or
6.62mL?
6.6mL
So there are 2 significant digits in your measurement
21. SIGNIFICANT DIGITS
What is the volume of the graduated cylinder?
What digits are you absolutely sure about?
21.5mL or
21.50mL?
21.5mL
So there are 3 significant digits in your measurement
22. SIGNIFICANT DIGITS
If the scale says that your
sample is 30.69g, then
how many significant
digits are in this value?
4 significant digits
It is NOT 30.690g, because the scale is not accurate to 3 decimal places
You cannot be more accurate than what your
instrument allows.
