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Significant figures; also know as "SIG FIGS" are very easy to learn! By the time you're finished reading this page you will know what I mean.
The Number of Significant figures in your answer depends on the number of significant figures in your given data.
SIG FIGS IS ALL ABOUT RULES! HERE THEY ARE:
ZERO'S:
1. Zeroes placed before other digits are not significant: example: 0.0000023 only has 2 Significant figures.
2. Zeroes placed between other digits are always significant: example: 5008 has 4 significant figures.
3. Zeroes placed after other digits but behind a decimal point are significant: example: 2.90 has 3 significant figures.
4. Zeroes at the end of a number are significant only if they are behind a decimal point as in 3. Otherwise, it is impossible to tell if they are significant.
Example: If you have 43000 you are not 100% sure if there are 2, 3,4 or 5 significant figures
SO WHAT SHOULD YOU DO?
Put them into scientific notation!
ex. 4.300 x 10⁴ has 4 significant figures
4.30 x 10⁴ has 3 significant figures
4.3 x 10⁴ has 2 significant figures
SIG FIGS IS ALL ABOUT RULES! HERE THEY ARE:
ZERO'S:
1. Zeroes placed before other digits are not significant: example: 0.0000023 only has 2 Significant figures.
2. Zeroes placed between other digits are always significant: example: 5008 has 4 significant figures.
3. Zeroes placed after other digits but behind a decimal point are significant: example: 2.90 has 3 significant figures.
4. Zeroes at the end of a number are significant only if they are behind a decimal point as in 3. Otherwise, it is impossible to tell if they are significant.
Example: If you have 43000 you are not 100% sure if there are 2, 3,4 or 5 significant figures
SO WHAT SHOULD YOU DO?
Put them into scientific notation!
ex. 4.300 x 10⁴ has 4 significant figures
4.30 x 10⁴ has 3 significant figures
4.3 x 10⁴ has 2 significant figures
RULES OF MULTIPLICATION AND DIVISION:
In a calculation involving multiplication and division the number of significant figures in an answer should equal the least number of significant figures in any one of the numbers being multiplied or divided.
example:
1. 3.0m (2 sig figs) x 4.67m (3 sig figs) = 14 (2 significant figures)
2. 3000.0 km (5 sig figs) / 6.0 km (2 sig fig)
= 500 X *The answer cannot be 500 because it must only have 2 sig figs.
so we put it into scienctific notation
= 5.0 x 10 to the 2.
RULES OF ADDITION AND SUBTRACTION:
In a calculation involving addition and subtraction, the number of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
example:
1. 3.98 (2 decimal places) + 4.3 (1 decimal place) + 4.66565632 (8 decimal places) = 12.9 ( 1 decimal place)
2. 39.00 (2 decimal place) - 5.543 (3 decimal places) + 3.33 (2 decimal places) = 36.79 (1 decimal place)
* Even though it may seem tempting to make this answer 36.8, you CANNOT because you must have 2 decimal places according to the data that you received.
**IMPORTANT
-When doing multi-step calculations, keep at least one more significant figure in intermediate results than needed in your final answer!
For example: If your intermediate step gets you with 2 sig figs add a 3rd so there is no error at the end.
In a calculation involving multiplication and division the number of significant figures in an answer should equal the least number of significant figures in any one of the numbers being multiplied or divided.
example:
1. 3.0m (2 sig figs) x 4.67m (3 sig figs) = 14 (2 significant figures)
2. 3000.0 km (5 sig figs) / 6.0 km (2 sig fig)
= 500 X *The answer cannot be 500 because it must only have 2 sig figs.
so we put it into scienctific notation
= 5.0 x 10 to the 2.
RULES OF ADDITION AND SUBTRACTION:
In a calculation involving addition and subtraction, the number of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
example:
1. 3.98 (2 decimal places) + 4.3 (1 decimal place) + 4.66565632 (8 decimal places) = 12.9 ( 1 decimal place)
2. 39.00 (2 decimal place) - 5.543 (3 decimal places) + 3.33 (2 decimal places) = 36.79 (1 decimal place)
* Even though it may seem tempting to make this answer 36.8, you CANNOT because you must have 2 decimal places according to the data that you received.
**IMPORTANT
-When doing multi-step calculations, keep at least one more significant figure in intermediate results than needed in your final answer!
For example: If your intermediate step gets you with 2 sig figs add a 3rd so there is no error at the end.
THE SINS OF SIGNIFICANT FIGURES!
1. Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data.
2. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.
2. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.
HERE ARE SOME EXAMPLES:
- ab/c = ?, where a = 483 J, b = 73.67 J, and c = 15.67
- x + y + z = ?, where x = 48.1, y = 77, and z = 65.789
- m - n - p = ?, where m = 25.6, n = 21.1, and p = 2.43
UNCERTAINTY
Uncertainty is present when a value is measured using a measurement instrument for example; a ruler.
This means that the person using the instrument as well as the actually instrument is not exact so there is an UNCERTAINTY!
There are 2 ways of expressing uncertainty:
1. Absolute uncertainty: this is expressed in the same units as the measurement.
Ex: 3.5 cm +_ 0.2 cm
2. Relative Uncertainty: this is expressed as a percentage of the measurement.
Ex: 4.89 cm +_ 3 %
How to find relative uncertainty:
Relative Uncertainty = (Absolute uncertainty / Value of measurement) x 100
Ex. Value = 4.6 cm +_ 0.2 cm
0.2 cm/ 4.6 cm = 0.04
0.04 x 100 = 4%
There are 2 ways of finding uncertainty:
1. Sometimes uncertainty is written on the actually instrument:
Ex. on a gratuated cylinder it might say it has an uncertainty of 0.01 mL.
2. When uncertainty is NOT indicated:
uncertainty = 1/2 of the smallest measurement on the instrument.
Ex: If the measurement on a ruler is 34 mm and the smallest measurement is 1 mm
Uncertainty= 34 mm +_ 0.5 mm.
This means that the person using the instrument as well as the actually instrument is not exact so there is an UNCERTAINTY!
There are 2 ways of expressing uncertainty:
1. Absolute uncertainty: this is expressed in the same units as the measurement.
Ex: 3.5 cm +_ 0.2 cm
2. Relative Uncertainty: this is expressed as a percentage of the measurement.
Ex: 4.89 cm +_ 3 %
How to find relative uncertainty:
Relative Uncertainty = (Absolute uncertainty / Value of measurement) x 100
Ex. Value = 4.6 cm +_ 0.2 cm
0.2 cm/ 4.6 cm = 0.04
0.04 x 100 = 4%
There are 2 ways of finding uncertainty:
1. Sometimes uncertainty is written on the actually instrument:
Ex. on a gratuated cylinder it might say it has an uncertainty of 0.01 mL.
2. When uncertainty is NOT indicated:
uncertainty = 1/2 of the smallest measurement on the instrument.
Ex: If the measurement on a ruler is 34 mm and the smallest measurement is 1 mm
Uncertainty= 34 mm +_ 0.5 mm.