The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

The wavelength of a spectral line is measured as $589.3 \pm 0.2$ nm. What is the wavelength expressed with the correct number of significant figures and its uncertainty?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
	**Primary Concept**: Significant Figures and Uncertainty
	**Related Topics**: Measurement, Error Analysis
	**Prerequisites**: Understanding of significant figures and how they relate to measurement uncertainty.
## SOLUTION PATHWAY
**Given Information**:
	* Measured wavelength: $589.3$ nm
	* Uncertainty: $0.2$ nm

**Method & Steps**:
	1.  **Identify significant figures in the measurement**: The measured value of 589.3 nm has four significant figures.
		Reasoning: All non-zero digits are significant, and zeros between non-zero digits are also significant.
	2. **Determine the number of decimal places in the uncertainty**: The uncertainty, 0.2 nm, has one decimal place.
		Reasoning: The uncertainty should be given to one or two significant figures, and typically rounded to the same decimal place as the measurement.
	3. **Express the measurement with the correct significant figures to match the uncertainty**: The measured value should be expressed with the same number of decimal places as the uncertainty. In this case, the measurement should have 1 decimal place, which it already does.
		Working: The measurement 589.3 nm already has one decimal place so no change is required.
	4. **Combine the measurement and uncertainty**: Express the result as measurement ± uncertainty.
		Result: $589.3 \pm 0.2$ nm
		Verification: The measurement and its uncertainty are expressed to the correct decimal places.
 ## OPTION ANALYSIS
[A] :x: [The uncertainty is not given and there should be four significant figures in the measurement.]
[B] :x: [The uncertainty is given with two decimal places which is incorrect, and the measurement is given with an extra decimal place.]
[C] ✓: [The measurement and uncertainty are correctly given with the appropriate number of significant figures and decimal places.]
[D] :x: [The measurement has been rounded and the uncertainty is not given. The measurement should have one decimal place, and not be rounded to the nearest whole number.]
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Incorrectly rounding the measurement before considering the uncertainty. The measurement should only be rounded to match the uncertainty.
		2.[Error 2]:  Not considering the number of decimal places when expressing the uncertainty. The uncertainty should have the same number of decimal places as the measurement.
	**Quick Tips**:
		1.[Helpful shortcut]: The uncertainty dictates the precision of the measurement; the measurement should have the same decimal place as the uncertainty.
		2.[Memory aid]: Always round the measurement to match the decimal places of the uncertainty.

Mr. ANIL KUMAR.G · Answer

$589 \pm 0$ nm

Mr. ANIL KUMAR.G · Answer

$589.30 \pm 0.20$ nm

Mr. ANIL KUMAR.G · Answer

The correct Option is "$589.3 \pm 0.2$ nm"

Mr. ANIL KUMAR.G · Answer

$590 \pm 0$ nm

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