sig figs
The digit itself as well as its placement in a number determines whether it is significant of not. Here are the rules:
1. Digits from 1-9 are always significant
2. Zeros placed between two other significant digits are always significant
3. Zeros to the right of a decimal or squished between another significant digit and a decimal are significant.
ex: 23.0 --> the zero is significant because it indicates a measurement with more precision than just 23 units
ex: 860. -->860 would normally only have 2 sig figs, but adding the decimal makes it significant. Any number that follows the decimal would only be making it more accurate.
4. Zeros used for spacing a decimal point are placeholders and are NOT significant
ex: 0.0035 --> only has 2 sig figs; 3 and 5
ex: 6700 --> only has 2 sig figs; 6 and 7
5. Numbers that are not measurements are NOT significant
-any thing counted
-constraints
-constants
ex: 3 pairs of shoes (no sig figs there)
ex: area of a triangle is bh/2 (the 2 is not a sig fig, but the measurements of the base and height are)
1. Digits from 1-9 are always significant
2. Zeros placed between two other significant digits are always significant
3. Zeros to the right of a decimal or squished between another significant digit and a decimal are significant.
ex: 23.0 --> the zero is significant because it indicates a measurement with more precision than just 23 units
ex: 860. -->860 would normally only have 2 sig figs, but adding the decimal makes it significant. Any number that follows the decimal would only be making it more accurate.
4. Zeros used for spacing a decimal point are placeholders and are NOT significant
ex: 0.0035 --> only has 2 sig figs; 3 and 5
ex: 6700 --> only has 2 sig figs; 6 and 7
5. Numbers that are not measurements are NOT significant
-any thing counted
-constraints
-constants
ex: 3 pairs of shoes (no sig figs there)
ex: area of a triangle is bh/2 (the 2 is not a sig fig, but the measurements of the base and height are)
Working with sig figs:
-When adding or subtracting numbers, the answer is rounded to the least number of decimal places
-When multiplying or dividing numbers, the answer is rounded to the least number of sig figs
*this least number of significant figures you are matching your answer to comes from the measurements in the problem or equation.
-When adding or subtracting numbers, the answer is rounded to the least number of decimal places
-When multiplying or dividing numbers, the answer is rounded to the least number of sig figs
*this least number of significant figures you are matching your answer to comes from the measurements in the problem or equation.
uncertainty
Uncertainty is present any time a measurement has been taken with an instrument. In other words, there is always some degree of uncertainty in a measurement.
There are 2 ways of expressing uncertainty:
Absolute uncertainty: where the uncertainty is expressed in the same units as the measurement.
5.7 cm + 0.3 cm
Relative uncertainty: where the uncertainty is expressed in a percent of the measurement
5.7 cm + 5%
relative uncertainty is calculated:
relative uncertainty = absolute uncertainty x 100
value of measurement
There are 2 ways of expressing uncertainty:
Absolute uncertainty: where the uncertainty is expressed in the same units as the measurement.
5.7 cm + 0.3 cm
Relative uncertainty: where the uncertainty is expressed in a percent of the measurement
5.7 cm + 5%
relative uncertainty is calculated:
relative uncertainty = absolute uncertainty x 100
value of measurement
Determining the uncertainty of a measurement
1- read the instrument for its uncertainty. Sometimes it is indicated
2- Half of the smallest measurement. If it is not indicated, take half the amount of the smallest measurement given buy the instrument. This is the uncertainty.
ex: a cylinder graduated in ml....the uncertainty would be + 0.5 ml
1- read the instrument for its uncertainty. Sometimes it is indicated
2- Half of the smallest measurement. If it is not indicated, take half the amount of the smallest measurement given buy the instrument. This is the uncertainty.
ex: a cylinder graduated in ml....the uncertainty would be + 0.5 ml