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Significant Figures
Significant figures are numbers recorded as a result of measured data gathered in
laboratory and calculations made as a result of that data. The data is always all
measured numbers plus the doubtful/limit of accuracy of the instrument.
Rule 1.
All non-zero digits are significant.
65,437
(5 sig. figs)
.198
(3 sig. figs.)
8.26
(3 sig. figs.)
Rule 2. All zeros to the left of non zero digits are place holders and not significant.
.008
(1 sig. fig)
0.8419
(4 sig. figs.)
0.00000000000000000008419
(4 sig. figs.)
Rule 3. All zeros between non zero digits or between significant figures are significant.
65007
(5 sig. figs)
.108
(3 sig. figs.)
8.00006
(6 sig. figs.)
800.003
(6 sig. figs.)
Rule 4. All zeros to the right of non zero digits AND to the right of the decimal point
are significant.
65.000
(5 sig. figs)
.100
(3 sig. figs.)
8.00000
(6 sig. figs.)
800.000
(6 sig. figs.)
Rule 5. All zeros to the right of non zero digits BUT NOT to the right of the decimal
point are UNKNOWN in significance. The number must be expressed in
standard scientific notation for clarity.
45,000
4.5 x 104 if 2 significant figures were intended
4.50 x 104 if 3 significant figures were intended
4.500 x 104 if 4 significant figures were intended
4.5000 x 104 if 5 significant figures were intended
Significant Figures
Significant figures in calculations.
1. Add/Subtract
In adding/subtracting measurements, round the answer to the lowest decimal place.
8.91
15.8106
24.7206
2 decimal places
4 decimal places
result must be rounded to 2 decimal places
24.72 is the proper answer.
2. Multiply/Divide
When multiplying/dividing, the answer may not have any more significant figures
than the measurement with the least number of significant figures.
16.74/2.6 = 6.43861538 (calculator display)
= 6.4 (proper answer)
Exact numbers: any number that is a counted number, or given in a definition, are
considered exact numbers and do not influence the judgement of significant figures.
3. Rounding with exact 5.
if the number to the right of the number being considered for rounding is exactly 5,
the number to be rounded goes up 1 if odd, but does not go up if it is even.
14.55000 rounded is 14.6
5 rounds up: it is odd and 5000 is exactly 5
14.55001 rounded is 14.6
5 rounds up. 5001 is greater than 5000
14.45000 rounded is 14.4
4 does not round:it is even, 5000 is exactly 5
14.45001 rounded is 14.5
5 rounds up. 5001 is greater than 5000
14.65000 rounded is 14.6
6 does not round:its even, 5000 is exactly 5
14.35000 rounded is 14.4
4 rounds up: it is even and 5000 is exactly 5