What Is Uncertainty in Measurement Definition Types Formula and Examples
All the measurements have a certain degree of uncertainty regardless of their precision and accuracy. This is because of two factors, the limitation of the measuring instrument (called systematic error) and the skill of the experimenter doing the measurements (called random error). Too often, we come across values that are very close to each other and their average values. In such cases, we can say that the measurement is correct and precise. Specifying the uncertainty formula chemistry is important as it will help us to study the overall effect on output.
Scientific Notation
As we are aware of the fact that atoms and molecules have extremely low masses, but they are present in large numbers.
Chemists deal with figures which are as small as 0.00000000000000000000000166 g (Mass of Hydrogen atoms) and other constants that have very large values, like Avagadros number, Planck’s constant, Speed of light, Charge of particles, etc. Now the question arises how to handle such small and large numbers?
To handle these large or small numbers, we use the following notation: x x 10\[^{y}\], which is, x times ten raised to the power of y. In this expression, y is an exponent having positive or negative values and x is that number that can vary from 1.000… and 9.999…
In the same way, scientific notation 823.912 can be written as 8.23912 x 10\[^{2}\]. In this, the decimal is moved to the left side by two places and if it is moved three places to the left then the power of 10 will be 3. In the same manner, 0.00065 can be written as 6.5 x 10\[^{-4}\]. In this, the decimal is moved four places towards the right, so, −4 is the exponent in the scientific notation.
[Image will be Uploaded Soon]
Uncertainty Calculation
Uncertainty in Multiplication and Division:
Applying the same rule as discussed above we can solve the given problem as:
(4.3 x 10\[^{7}\]) x (2.7 x 10\[^{3}\]) = (4.3 x 2.7)(10\[^{7+3}\])
= (4.3 x 2.7) (10\[^{10}\])
= 11.6 x 10\[^{10}\]
Similarly for division,
\[\frac{4.9 \times 10^{-4}}{3.2 \times 10^{-6}}\] = (4.9 ÷ 3.2)(10\[^{-4-(-6)}\]) = 1.531 x 10\[^{2}\]
Uncertainty in Addition and Subtraction:
While doing addition or subtraction first of all we have to place these numbers in such a way that they have the same exponents. Eg: If there are two numbers 7.32 x 10\[^{3}\] and 9.55 x 10\[^{2}\]
Now adding both 7.32 x 10\[^{3}\] + 9.55 x 10\[^{2}\] = (7.32 + (0.955 x 10)) x 10\[^{3}\] = 8.275 x 10\[^{3}\]
Similarly for subtraction,
7.32 x 10\[^{3}\] - 9.55 x 10\[^{2}\] = (7.32 - (0.955 x 10))10\[^{3}\] = 6.365 x \[^{3}\]
Percentage Uncertainty Formula:
The uncertainty of a measured value can be represented in a percentage notation or as a simple ratio. It is calculated as:
percent uncertainty = \[\frac{Uncertainity}{\text{Actual value}}\] x 100
Solved Examples
Example: A scale measures wrongly a value as 6 cm due to some marginal errors. If the actual measurement of the value is 10 cm then calculate the percentage error.
Solution: Given,
Approximate value/wrong value = 6 cm
Exact value = 10 cm
Percentage Error = (Approximate Value - Exact Value)/Exact Value) x 100
Percentage Error = (10 – 6)/10 × 100
= 40 %
FAQs on Uncertainty in Measurement in Chemistry Explained Clearly
1. What is uncertainty in measurement in chemistry?
Uncertainty in measurement is the estimated range within which the true value of a measured quantity is expected to lie. In chemistry, every experimental measurement (mass, volume, temperature, concentration) has some degree of measurement uncertainty due to instrument limitations and human error.
- It is usually written as: measured value ± uncertainty (e.g., 25.0 ± 0.1 mL).
- It reflects the precision of the measuring instrument.
- Uncertainty does not mean a mistake; it shows the reliability of the measurement.
2. Why is uncertainty in measurement important in chemistry experiments?
Uncertainty in measurement is important because it indicates the reliability and precision of experimental results in chemistry. Without stating uncertainty, numerical data such as molarity, mass, or volume are incomplete.
- It helps compare experimental values with theoretical values.
- It shows whether differences between results are significant.
- It improves accuracy in stoichiometric and titration calculations.
3. What is the difference between accuracy and precision in measurement?
Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other. These are related but different concepts in analytical chemistry.
- Accuracy depends on systematic errors.
- Precision depends on random errors and instrument consistency.
- A result can be precise but not accurate, or accurate but not precise.
4. How do you calculate percentage uncertainty?
Percentage uncertainty is calculated using the formula (absolute uncertainty ÷ measured value) × 100%. This expresses uncertainty relative to the size of the measurement.
- Step 1: Identify the absolute uncertainty (e.g., ±0.1 g).
- Step 2: Divide by the measured value (e.g., 10.0 g).
- Step 3: Multiply by 100%.
5. What is absolute uncertainty in chemistry?
Absolute uncertainty is the margin of error expressed in the same units as the measured value. It represents the possible variation in a single measurement.
- Example: 50.0 ± 0.2 mL has an absolute uncertainty of 0.2 mL.
- It depends on the smallest scale division of the measuring instrument.
- It is commonly half the smallest scale reading for analog instruments.
6. How do uncertainties combine when adding or subtracting measurements?
When adding or subtracting measurements, absolute uncertainties are added together. This rule applies in error propagation for sums and differences.
- Example: (25.0 ± 0.2) mL + (10.0 ± 0.1) mL
- Total volume = 35.0 mL
- Total uncertainty = 0.2 + 0.1 = ±0.3 mL
7. How do uncertainties combine when multiplying or dividing measurements?
When multiplying or dividing measurements, percentage (or fractional) uncertainties are added. This rule is used in calculations involving density, molarity, and concentration.
- Step 1: Convert each absolute uncertainty to percentage uncertainty.
- Step 2: Add the percentage uncertainties.
- Step 3: Apply the total percentage to the final result.
8. What are the main types of errors that cause uncertainty in chemistry?
The main types of errors that cause uncertainty in chemistry are systematic errors and random errors. These affect measurement reliability in different ways.
- Systematic errors: consistent errors due to faulty equipment or calibration (affect accuracy).
- Random errors: unpredictable variations in measurement (affect precision).
- Human reading errors and environmental factors can contribute to both.
9. How do significant figures relate to uncertainty in measurement?
Significant figures reflect the precision of a measurement and indicate its uncertainty. The number of significant figures reported depends on the measuring instrument.
- The last significant figure is considered uncertain.
- A balance reading 2.34 g implies uncertainty of about ±0.01 g.
- Results of calculations must be rounded to match the correct significant figures.
10. Can you give an example of uncertainty in a chemistry measurement?
An example of uncertainty in chemistry is measuring 25.0 mL of solution with a measuring cylinder that has ±0.5 mL uncertainty. The measurement is written as 25.0 ± 0.5 mL.
- This means the true volume lies between 24.5 mL and 25.5 mL.
- The percentage uncertainty is (0.5 ÷ 25.0) × 100% = 2%.
- This uncertainty affects calculations such as molarity (M = moles ÷ volume in L).
