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Q.176 Physics ⭐ 360° Option Elimination Active
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NEET 2020 Physics Question 176 Solution

Topic: Units and Measurements · Official NTA Booklet Code E1
NEET 2020 Physics Question 176: Significant Figures in Arithmetic Subtraction

Question

Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 m?

✓
Verified Against NTA Final Answer Key
Option (2) : 9.98 m
📚 Units and Measurements Easy
📋 Given Parameters & Problem Setup
Measurement 1 9.99 m (2 decimal places)
Measurement 2 0.0099 m (4 decimal places)
⚡

The 30-Second Exam Hall Shortcut: ⚡ "Rule for addition/subtraction: Result must have the same number of decimal places as the least precise number (2 decimal places). 9.99 - 0.0099 = 9.9801 m -> rounds to 9.98 m!"

⏱️ 20 seconds

In addition and subtraction, the final result must retain as many decimal places as there are in the number with the least decimal places. In 9.99 m, there are 2 decimal places. In 0.0099 m, there are 4 decimal places. The subtraction 9.99 - 0.0099 = 9.9801 m must be rounded off to 2 decimal places, yielding 9.98 m. Mark Option (2) in 3 seconds!

1 Check decimal places: 9.99 m has 2 decimal places; 0.0099 m has 4 decimal places.
2 Least number of decimal places = 2.
3 Subtract mathematically: 9.9900 - 0.0099 = 9.9801 m.
4 Round to 2 decimal places: 9.9801 rounds to 9.98 m.
5 Select Option (2).
🛡️
Why You Can 100% Trust This Shortcut: NCERT Physics · Units and Measurements (Rules for Arithmetic Operations with Significant Figures)
📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Rule for Significant Figures in Subtraction

For addition and subtraction of experimental measurements: 'The final result should retain as many decimal places as there are in the number with the least decimal places.'

Step 2

Identify Decimal Precision of Terms

- In 9.99 m9.99\text{ m}, there are 2 digits after the decimal point. - In 0.0099 m0.0099\text{ m}, there are 4 digits after the decimal point. The result must therefore be restricted to 2 decimal places.

Step 3

Perform Mathematical Subtraction

9.9900−0.0099=9.9801 m9.9900 - 0.0099 = 9.9801\text{ m}.

Step 4

Apply Rounding Off to 2 Decimal Places

Looking at the third decimal digit in 9.98019.9801: it is 00 (<5< 5), so the preceding digit (88) remains unaltered. Rounded result = 9.98 m9.98\text{ m}. Matches Option 2.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan
1 A
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; retains all mathematical digits without applying experimental significant figure rules.

⚠️
Student Fallacy (Why candidates pick this trap): Ignoring significant figure rules entirely.
2 B
✓ 100% Correct
Verdict & Scientific Reason:

Accurate value; rounded to 2 decimal places to match the least precise measurement (9.99 m).

💡
Why this is airtight: None; rigorous application of NCERT rounding rules.
3 C
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; has 3 decimal places instead of 2.

⚠️
Student Fallacy (Why candidates pick this trap): Keeping an extra decimal place.
4 D
✗ Incorrect
Verdict & Scientific Reason:

Incorrect; reduced to 1 decimal place unnecessarily.

⚠️
Student Fallacy (Why candidates pick this trap): Over-rounding.
⚠️

NTA Trap Alert: Decimal Places vs Significant Figures

Addition/subtraction is governed by the LEAST NUMBER OF DECIMAL PLACES, not least total significant figures. (Multiplication/division uses total significant figures).

🛡️ How to avoid the -1 mark: For + or -, count digits after the decimal point!
📖

Core NEET Syllabus Standard

Physics · Units and Measurements Standard Benchmark
Core Scientific Principle Tested:

""

Syllabus Focus: Significant Figures in Arithmetic Subtraction
✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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