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SIGNIFICANT FIGURES RULES
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Terms in this set (13)
SIGNIFICANT FIGURES
the reliable digits in a measurement based on the accuracy of the measuring device
RULE #1
Nonzero digits are always significant
32445 5 sig figs
0.23435 5 sig figs
2348.23 6 sig figs
RULE #2
Zeros are weird and come in 3 flavors
FLAVOR 1
FLAVOR 2
FLAVOR3
FLAVOR 1 RULE #2.1
OF ZEROS IS CALLED
Leading Zeros
These precede non-zero digits and don't count. They are only placeholders.
0.0023 2 sig figs
0.02300 4 sig figs
FLAVOR 2 RULE #2.2
OF ZEROS IS CALLED
Captive Zeros
These are between nonzero digits. They always count as sig figs.
1.009 4 sig figs
230,004 6 sig figs
FLAVOR 3 RULE #2.3
OF ZEROS IS CALLED
Trailing Zeros
These are zeros at the right end of the number. They are significant only if the number has a decimal point.
100 = 1 sig fig
1.00 x 102 = 3 sig figs
100. = 3 sig figs
RULE #3
EXACT NUMBERS
These are non-measured
numbers (8 atoms),
10 molecules = infinite sig figs
numbers in formulas 2(PIE SIGN)r2
4/3(PIE SIGN)3 = infinite sig figs
numbers from definitions (1 in=2.54 cm).
Exact numbers have an infinite number of sig figs.
(PIE SIGN) = infinite sig figs
Addition & Subtraction
The answer must have as many decimal places as the measurement having the least number of decimal places.
12.11 12.11005
18.0 0.0004
+ 1.013 - 1.0
_________ ___________
31.123 = 31.1 11.10965 = 11.1
Multiplication & Division
The answer may contain only as many significant digits as the measurement with the least number of significant digits
4.56 X 1.4 = 6.38 6.4
3 sig figs 2 sig figs 2 sig figs
19.03 divided by 10 = 1.903 which equals 2
4 sig figs 1 sig fig 4 sig figs 1 sig fig
Rule 1 FOR ROUNDING
If the digit to be removed is less than 5, the preceding digit stays the same; if it is equal to or greater than 5, round the preceding digit up. Ignore all other numbers.
3.04999 = 3.0
3.05999 = 3.1
Rule 2 FOR ROUNDING
In a series of calculations, carry the extra digits through to the final result, THEN round
3.05 x 5.555 x 3.0 = 50.82825 = 51
NOT
3.1 x 5.6 x 3.0 = 52.08 = 52
GENERAL INFO ON SIG FIGS
Sig figs give you information on the EXACTNESS of a measurement
Use sig figs ONLY when you are measuring something (ie not counting it). 36 students has an infinite number of sig figs.
Ignore the number of sig figs in equations (A=bh/2) or definitions 1m = 1000mm
MORE INFO ON SIG FIGS
All digits in numbers written in scientific notation are significant (3.4543x104 has 5 sig figs)
When measuring, ONLY ONE estimated digit is allowed to be significant
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