Rounding

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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 dont 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 Lets take a look a technique that will
help us figure it out
Its 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

• 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
Lets try some examples. How many
significant Figures are in the following numbers?
4 sig figs
3456
0.040860
5 sig figs
6 sig figs
3.50001

1 sig fig
20000
7 oranges
Infinite sig figs
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Atlantic Pacific Rule
Lets try some more examples. How many sig
figs Are there in the following pairs of numbers?
750 vs. 750.
2 vs 3 sig figs
4 vs. 1 sig figs
1001 vs. 1000
3 vs. 4 sig figs
2.07 vs. 2.070

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
Its important we know how to manipulate
Significant figures. Well 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
Lets 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