Transcript Significant Figures

Mr. Shields
Regents Chemistry U00 L02
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Significant Figures
In all numbers there are digits that are Significant
& others are not Significant.
Why should we be concerned which
numbers are significant?
1) Measurements are never exact.
2) Scientist want to record their data (nos.) with the
LEAST AMOUNT OF UNCERTAINTY.
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Significant Figures
Scientists created rules so numbers could be written
with the least amount of uncertainty. These are the
rules governing what are called Significant figures.
By using these rules scientist can be confident that the
numbers people report don’t exaggerate their accuracy!
The greater the number of significant figures the more
PRECISE the number
For example 3.41 is less precise than 3.413341
There are more sig figs in the 2nd number
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Significant Figures
To determine the number of significant figures in a number
Let’s take a look a technique that will help us figure it out
It’s called the ATLANTIC - PACIFIC RULE
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Atlantic – Pacific Rule
1. Draw a map of the United States and label
the 2 oceans … which are???
PACIFIC
ATLANTIC
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Atlantic – Pacific Rule
1. If a decimal point is Present in the number
start counting from the Pacific side
2. If a decimal point is Absent in the number
count from the Atlantic side
3. Begin counting all numbers from the first
NON-ZERO digit
- That number and all digits after it
(including zeros) are SIGNIFICANT
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Try the rule with these two numbers. How many
Sig figs are there?
0.06901
100,100,300
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Significant Figures
Lastly, all COUNTING and DEFINED NUMBERS are
treated as if they have an INFINITE no. of Sig Figs
Ex: 2 pairs of gloves
Counting
(infinite sig fig)
7 Keys
Counting
“
2.54 cm = 1 inch
Definition
“
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Atlantic – Pacific Rule
Let’s try some examples. How many significant
Figures are in the following numbers?
3456
4 sig figs
0.040860
5 sig figs
3.50001
6 sig figs
20000
1 sig fig
7 oranges
Infinite sig figs
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Atlantic – Pacific Rule
Let’s try some more examples. How many sig figs
Are there in the following pairs of numbers?
750 vs. 750.
2 vs 3 sig figs
1001 vs. 1000
4 vs. 1 sig figs
2.07 vs. 2.070
3 vs. 4 sig figs
0.00572 vs 572 3 vs. 3 sig figs
1001. vs. 1000. 4 vs 4 sig figs
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Working with Significant Figures
It’s important we know how to manipulate Significant
figures. We’ll need to know the same manipulations
we needed to know for Scientific Notation, namely:
1. Addition
+
2. Subtraction
-
3. Multiplication
x
4. Division
/
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Working with Significant Figures
Let’s look at the rules that govern these mathematical
operations.
1 & 2. Addition & Subtraction have the same rule
The number of decimal places in the Ans. EQUALS the
Smallest Number of DECIMAL places in any of the nos.
Being added or subtracted.
Ex: 6.8 + 11.934 = 18.734
= 18.7
2.01 + 0.003 + 1 = 3.013
=3
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Working with Significant Figures
3 & 4. Multiplication & Division have the same rule
The number of sig figs in the ans. Equals the number of
Sig Figs in the least precise number
Ex: 6.8 x 11.934 = 81.1512
= 81.
2.014 / 0.70 = 2.877143
= 2.9
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