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Significant figures
Rounding to n significant figures is a form of rounding. Using Significant Figures (a.k.a Sig-Figs)
to round numbers is a more general form of rounding than to a specific number of decimal
places. In mathematical operations involving significant figures, the answer is reported in such a
way that it reflects the reliability of the least precise operation.
Identifying significant digits
1. All non-zero digits are significant. Example: '123.45' has five significant figures: 1,2,3,4 and 5.
2. Zeros appearing in between two non-zero digits are significant. Example: '101.12' has five
significant figures: 1, 0,1,1,2.
3. All zeros appearing to the right of an understood decimal point and non-zero digits are
significant. Example: '12.2300' has six significant figures: 1, 2,2,3,0 and 0. The number
'0.00122300' still only has six significant figures (the zeros before the '1' are not significant).
4. All zeros appearing in a number without a decimal point and to the right of the last non-zero
digit are not significant unless indicated by a bar. Example: '1300' has two significant figures: 1
and 3. The zeros are not considered significant because they don't have a bar. However, 1300.0
has five significant figures.
Sig-Figs can either be rounded up or down and are used in all four operations.
For e.g. - if you were asked to round of the number 6784.87876 to 5 significant figures what
would it be.
In the above number 6, 7,8,4,8 are the first five significant numbers. 7 being the sixth figure
must be rounded up because it is greater than five. Hence the rounded figure would be 6784.9
Here are some problems1. 456.8; 3 sig figs
457
2. .00067; 4 sig figs
.0007
3. 19,840; 3 sig figs
19,800
4. 25.05; 2 sig figs
25
5. 4567; 1 sig fig
5000
When adding or subtracting, the final answer must be rounded to the correct number of sig
figs. When rounding it to sig figs the answer cannot have more digits than the least accurate
number.
For e.g.
150.0
+
0.507
150.5
In the above problem 150.0 is considered less accurate than 0 .507. Draw an imaginary line
after the .0 in 150.0. That is where you need to round of the figure to number of sig figs. As the
number of digits increase from left to right, the number with more digits after the decimal point
is considered more accurate.
2.67
+ .845
3.52
2.67 + .845= 3.515. But the least accurate number is 2.67 and an imaginary vertical line can be
drawn at 7. This is where you round of the answer.
Here are some problems6. 20.7 + 40.2 = 60.9
7. 84.567 + 5.999453 = 90.566
8. 65.2+.66666666 = 65.9
9. 78 + 2304.78 = 2383
Sig figs can also be used for multiplication and divisions. In these kinds of problems the answer
is rounded to the number with least number of sig figs
For e.g. -
24.08
X 7.0976
170.9
In the above question 24.08 has 4 sig figs and 7.0976 has 5 sig figs. Therefore the answer must
be rounded to 4 sig fig.
Here are some problems10. 3.461/ 5.61 = 9.07
11. 1.245 x 45.78 x .089= 5.07
12. .0005 x 6.789 x 459 = 2
13. 2.089 x 534.10= 1116
If there is a problem which involves addition and multiplication always use the multiplication
rule to round off the number to the correct sig figs.
For e.g.(24 + 56.002 + 67.6 + 567.7 + 5.45)/5
=100