Significant Figures
Significant Figures
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Significant Figures Notes – Physical Science
1. Significant figures apply to measured values.
They are significant to the measurement NOT to
the number.
2. The number of significant figures is determined
by the resolution of the instrument used to make
the measurement.
The last digit in a measured number is always
the “estimated” digit.
Rules for Counting Significant
Figures
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Non-zero numbers are ALWAYS
significant.
Example: 312cm and 0.546mm both
3
have ______
significant figures
Sig. Fig. Rules - continued
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Leading Zeros are NEVER significant.
2 significant
Example: 0.000047pm has _____
figures.
consider this number in scientific notation:
4.7 x 10-5
How many significant figures?
Sig. Fig. Rules - continued
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Captured Zeros , zeros between two
non zero numbers, are ALWAYS
significant.
Example: Both 4,005km and 40.05dm
4
contain ______
significant figures.
Sig. Fig. Rules - continued
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Trailing Zeros are only significant if
they are present with a decimal place.
2
Example: 120mL has _____
sig. figs.
4
120.0mL has _____
sig. figs.
Which number was measured with the
more accurate volumetric measuring
device?
Sig. Fig. Rules - continued
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Significant figures DO NOT APPLY to
“counted” or “exact” numbers or
definitions.
Examples: 1 inch = 2.54 cm has NO sig. Fig.
14 pencils has NO sig figs.
You do not use these numbers to determine
the number of sig figs in your answer
Significant Figures Rules Summary
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Non-zero numbers – Always Significant
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Captured zeros – Always Significant
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Leading zeros – Never Significant
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Trailing zeros – Only with a decimal
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Counted numbers – does not apply
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Numeric Definitions – does not apply
Rounding Rules
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Rule 1 - if the remainder beyond the last
digit to be reported is less than 5, drop the
numbers past the last digit.
Example: Rounding to one decimal place, the
number 5.3467 becomes 5.3.
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Rule 2 - if the remainder is equal or
greater than 5, increase the final digit by 1.
Example: The number 5.798 becomes 5.8 if
rounding to 2 digits.
4.025 becomes 4.03 if rounding to 3 digits.
Multiplying/Dividing with
Significant Figures:
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The answer will have the same number of
sig figs as the number with the least sig.
figs in the calculation.
153
Example: 30 x 5.1 =
_______
1 sig fig so the answer
BUT: 30 has only ____
1 sig fig.
can only have _____
200
The correct answer is _____
Adding/Subtracting with
Significant Figures
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The answer will have the same number of
decimal places as the number with the least
decimal places in the calculation.
334.54
Example: 331.34 + 3.2 = ___________
BUT 3.2 has only one decimal place so the
334.5
rounded answer is ______
Practice –
How many significant figures?
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46 marbles
3.02 x 102 cm
0.003407 in.
230 mL
2.4cm x 3.21cm
5.66mL + 1.234mL
6.02 x 1023 atoms
None
3
4
2
2
3
None