Transcript Significant Figures

Significant Figures
Certain or good estimates of the
numbers
Note:
• No measurement is exact
• Uncertainty exists in all measurement
Refer to fig 5.5 0n page 122
• What is the length of the pin?
 Between 2.8 and 2.9
• Consider the data below
person
measurement
1
2.85
2
2.84
3
2.86
4
2.85
5
2.86
In the given measurements
which numbers are certain?
Which number is uncertain?
What does it mean ?
• 1.86 + 0.01kg
means 1.86 + 0.01 = 1.87
1.86 – 0.01 = 1.85
Rules for significant Figures
• All nonzero digits are significant(1,2,3…)
• Zeros that precede all of the non zero digits are not significant Ex:
0.0025
 2 significant figures
• Zeros between nonzero digits are significant
Ex 1.008
 4 significant figures
• Zeros at the right end of a number is significant if there is decimal
point Ex: 23.00
 4 significant figures
Ex : 100
 1 significant figure
Pacific Atlantic Rule
•
•
If the decimal point is present in a given measurement, start from the pacific or left
side. Start counting from the first nonzero digit and the zeros all the way at the end
are considered significant figure
Ex: 0.00560
25.100
0.500
0.00560 - 3 sig. fig
25.100 – 6 sig. fig.
0.500 – 3 sig.fig
If the decimal point is not present in a given measurement, start from the Atlantic
(right side). Start counting from the first nonzero digit and the zeros all the way at end
are considered significant figure.
Examples:
125, 100
100
210,000
125, 100
- 4 sig.fig.
100 – 1 sig.fig.
210,000 2 sig.fig
How many significant figures are
there?
•
•
•
•
•
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0.00251
12.380
0.0205
260.0
20.56
123 000

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

3
5
3
4
4
3
Rounding off numbers using
significant figures( p.127)
• Multiplication & division
 round off the answer with the least number of
significant figures
Ex: 4.56 x 1.4 = 6.384
 6.4
• Addition and Subtraction
 Round off the answer with the smallest decimal places
Ex: 12.11 + 18.0 + 1.013 = 31.123
 31.1
Systems of Units
• British or English System
 Known as FPS ( F-Foot , P – Pound and S- second)
• Metric System
 Called International System of Units or SI units
 Known as MKS -- M-meter, K-kg , s second
CGS -- C- cm , G- grams, s- second
Note: Ancient people used units of measurement using body parts.
These cannot be considered standard units because they vary from
person to person. To eliminate such confusion, they agreed to use
standard units like grams for mass, meter for distance, seconds for
time and etc.
5.6 Problem solving and
dimensional analysis ( p. 130)
• Conversion of units
Dimensional analysis
- to cancel out units other than the desired unit
through the used of fixed relationship or
conversion factor
Unit sought for = unit given x conversion factor
Ex: convert 3.6 km to meters
Solution: Conversion Factor(C.F.) –>1km = 1000m
3.6km x 1000m = 3600m
1km
Conversion Factors
Length
1meter(m)
= 100 cm
1kilometer(km) =1000m
1centimeter(cm) = 10mm
1inch(in)
=2.54cm
1foot (ft)
= 12 in
1mile(mi)
= 1.61km
1meter(m)
= 39.37in
Mass
1kilogram(kg) = 1000g
1 pound (lb) = 453.59g
1 pound
= 16ounces
1kilogram
= 2.2 lbs
Examples
•
Convert the following measurements
a)
800m  km
c) 30m  in
b)
300ft  in
d) 650lbs  kg
Solution:
a) Conversion factor : 1km or 1000m
100m
1km
800m x 1km
= 0.8km
1000m
c)Conversion factor:
1m
or 39.37in
39.37in
1m
30m x 39.37in = 1181.1 in
1m
b) Conversion Factor: 1ft or 12in
12in
ift
300 ft x 12 in = 3600 in
1ft
d) Conversion factor: 1 kg = 2.2lbs
2.2 lbs
1kg
650 lbs x 1kg
= 295.45 kg
2.2lbs
More Examples
Convert 25mi to m
Conversion Factor:
1mi = 1.6km ---> can be expressed as 1mi or 1.6km
1.6km
1mi
1km = 100m ---> can be expressed as 1km
0r 100m
100m
1km
Solution: Convert mi to km then km to m
25mi x 1.6km = 40km
1mi
40km x 100m = 4000m therefore 25 mi = 4000m
1km
Ex: Convert 25 km to m
hr
s
Conversion factor : 1km = 100m
1hr = 3600s
Solution: Convert km to m and hr to s
Ex: Convert 30kg to g
L
mL
Conversion Factor : 1kg = 100g
1L = 1000mL
Solution: Convert kg to g and L to mL
25km x 100m = 25,000m
hr
1km
hr
30kg x 100g = 3000g
L
1kg
L
2500m x 1hr
= 0.69 m
hr
3600s
s
3000g x 1L . = 3 g
L
1000mL
mL
Practice Problems
• Convert 100m to km
s
hr
Convert 500ft to centimeter
Convert 2months to hours
Convert 750g to lbs
Convert your height into centimeter (cm)