Significant Figures NEET Notes: Rules, Tricks, Examples & Practice Questions

 - Dr.Sanjaykumar Pawar 

Significant Figures and Measurement Errors | NEET Smart Notes

NEET Smart Notes: Significant Figures Rules, Calculation Tricks and Quick Revision Guide

Internal Links

Units and Dimensions NEET Notes

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Measurement Errors and Accuracy NEET Notes

→ /measurement-errors-neet-notes

Scientific Notation and Powers of Ten

→ /scientific-notation-neet-notes

Important Class 11 Physics Formula Notes

→ /class-11-physics-formula-notes

NCERT Chemistry Chapter 1 Some Basic Concepts of Chemistry Notes

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NEET Physics Numerical Problems with Solutions

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NEET Chemistry Revision Notes PDF

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NEET Smart Notes: Significant Figures & Mass Calculation

Part 1: Question and Answer

Question:

The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. Find:

(a) The total mass of the box.
(b) The difference in the masses of the pieces to correct significant figures.

Solution:

Given:

• Mass of box = 2.30 kg
• Mass of gold piece 1 = 20.15 g
• Mass of gold piece 2 = 20.17 g

Step 1: Convert kg into grams

1 kg = 1000 g

2.30 kg = 2.30 × 1000 = 2300 g

(a) Total Mass of Box

Mass of gold pieces:

20.15 g + 20.17 g = 40.32 g

Total mass:

2300 g + 40.32 g = 2340.32 g

For addition, answer should have the same decimal places as the least precise value.

2340.32 g ≈ 2340 g

Final Answer (a): 2.34 kg

(b) Difference in Masses

20.17 g - 20.15 g = 0.02 g

Final Answer (b): 0.02 g

Part 2: Short Notes

Significant Figures

Significant figures are the meaningful digits present in a measurement. They indicate the accuracy and precision of a measurement.

Example:
2.30 kg has 3 significant figures.

Rules for Addition and Subtraction

In addition and subtraction, the number of decimal places decides the final answer.

Addition/Subtraction → Check Decimal Places

Example:
20.15 + 20.17 = 40.32

Unit Conversion

Before calculation, all quantities must be converted into the same unit.

1 kg = 1000 g

Steps to Solve Questions

1. Convert all quantities into the same unit.
2. Perform addition or subtraction.
3. Apply significant figure rules.
4. Write final answer with correct unit.

Part 3: Concept Table

Concept	Meaning	Example
Measurement	Finding the value of a physical quantity	Mass = 2.30 kg
Significant Figures	Meaningful digits in measurement	2.30 has 3 SF
Addition/Subtraction Rule	Decimal places decide answer	20.15 + 20.17
Unit Conversion	Change units before calculation	1 kg = 1000 g

Part 4: Memory Mnemonics

Mnemonic 1:

"ADD-SUB → Decimal Dekho"

Addition and subtraction में हमेशा decimal places count करो.

Mnemonic 2:

"MULTI-DIV → Significant Gino"

Multiplication and division में significant figures count करो.

Mnemonic 3: Zero Rule

"Between and Behind = Important, Before = Ignore"

• Between zeros → Significant
• Decimal के बाद ending zeros → Significant
• Starting zeros → Not significant

30-Second Revision Box

SIGNIFICANT FIGURES

Addition/Subtraction
        ↓
Decimal Places

Multiplication/Division
        ↓
Significant Figures

Zero Rules:
Between digits → Significant
After decimal → Significant
Before first digit → Not Significant

1 kg = 1000 g

Convert units before calculation.

NEET Physics: Precision & Least Count Practice Questions with Answers

 - Dr.Sanjaykumar Pawar

Comparison of measuring instruments showing how least count affects precision in Physics for NEET preparation.

 

CBSE Class 11 Physics Notes

Chapter: Units and Measurements

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Question

Which of the following is the most precise device for measuring length?

(a) A vernier callipers with 20 divisions on the sliding scale.

(b) A screw gauge of pitch 1 mm and 100 divisions on the circular scale.

(c) An optical instrument that can measure length to within a wavelength of light.

---

Step-by-Step Solution

Step 1: Find the Least Count of Vernier Callipers

20 Vernier Scale Divisions = 19 Main Scale Divisions

Least Count = 1 MSD − 1 VSD

LC = 1/20 mm

Least Count = 0.05 mm

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Step 2: Find the Least Count of Screw Gauge

Given:

• Pitch = 1 mm
• Circular Scale Divisions = 100

Least Count = Pitch ÷ Number of Circular Scale Divisions

LC = 1 ÷ 100

Least Count = 0.01 mm

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Step 3: Optical Instrument

Optical instruments measure length up to one wavelength of light.

Average wavelength of visible light

λ ≈ 5 × 10^-7 m
≈ 0.0005 mm

Therefore, Least Count ≈ 0.0005 mm

---

Step 4: Comparison

Instrument	Least Count
Vernier Callipers	0.05 mm
Screw Gauge	0.01 mm
Optical Instrument	0.0005 mm

Smaller Least Count = Greater Precision

0.0005 mm is the smallest.

Correct Answer: (c) Optical Instrument

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Complete Notes

1. Measurement

Measurement means comparing an unknown quantity with a standard quantity.

Examples

• Measuring length using a ruler.
• Measuring wire diameter using a screw gauge.
• Measuring pipe diameter using a vernier callipers.

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2. Least Count

Least Count is the smallest value that an instrument can measure accurately.

Smaller Least Count = Higher Precision

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3. Accuracy

Accuracy means how close a measured value is to the true value.

Example: Actual length = 10.00 cm Measured length = 10.01 cm This is highly accurate.

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4. Precision

Precision means how close repeated measurements are to each other.

Example

• 10.02 cm
• 10.01 cm
• 10.02 cm
• 10.01 cm

These readings are highly precise.

---

5. Difference Between Accuracy and Precision

Accuracy	Precision
Close to true value	Close to repeated values
Correctness	Repeatability

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6. Vernier Callipers

Uses

• External diameter
• Internal diameter
• Depth

Least Count = 1 MSD − 1 VSD

For 20 divisions, LC = 0.05 mm

---

7. Screw Gauge

Uses

• Diameter of wire
• Thickness of paper
• Metal sheet thickness

Pitch = Distance moved in one complete rotation.

Least Count = Pitch ÷ Circular Scale Divisions

Example
Pitch = 1 mm
Divisions = 100
LC = 0.01 mm

---

8. Optical Instrument

Uses light waves to measure extremely small distances.

Approximate precision

0.0005 mm

This is the most precise among the given instruments.

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9. Comparison of Measuring Instruments

Instrument	Least Count	Precision
Metre Scale	1 mm	Low
Vernier Callipers	0.05 mm	Better
Screw Gauge	0.01 mm	Very Good
Optical Instrument	0.0005 mm	Highest

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Important Formulas

Least Count (Screw Gauge)

LC = Pitch ÷ Number of Circular Scale Divisions

Least Count (Vernier Callipers)

LC = 1 MSD − 1 VSD

---

Quick Revision

• Measurement compares an unknown quantity with a standard.
• Least Count = Smallest measurable value.
• Smaller Least Count means Higher Precision.
• Accuracy = Closeness to true value.
• Precision = Closeness of repeated readings.
• Vernier Callipers LC = 0.05 mm.
• Screw Gauge LC = 0.01 mm.
• Optical Instrument LC ≈ 0.0005 mm.
• Most Precise Instrument = Optical Instrument.

Exam Tip:
Whenever you are asked to compare measuring instruments, always compare their least counts. The instrument with the smallest least count is the most precise.

CBSE Class 11 Physics | Units and Measurements | Complete Beginner Notes

NEET Smart Learning Structure

Topic: Precision of Measuring Instruments

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1. Exam Snapshot (30 Seconds Rule)

✔ Least Count जितना कम होगा → Precision उतनी अधिक होगी

Order:
Metre Scale → Vernier Callipers → Screw Gauge → Optical Instrument

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2. Visual Memory Table

Instrument	Least Count	Precision	Uses	NEET Keyword
Metre Scale	1 mm	Low	Basic length	Easy
Vernier Callipers	0.05 mm	Better	Diameter, Depth	Medium
Screw Gauge	0.01 mm	High	Wire thickness	Important
Optical Instrument	0.0005 mm	Highest	Atomic level	Advanced

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3. Memory Trick (Mnemonic)

Mnemonic: "मेरा वीर शेर ऑपरेशन करेगा"

म = Metre Scale
वीर = Vernier Callipers
शेर = Screw Gauge
ऑपरेशन = Optical Instrument

✔ Top to Bottom: Least Count ↓, Precision ↑

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4. Golden Rule

⭐ सबसे छोटा Least Count = सबसे अधिक Precision

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5. Formula Box

Vernier Callipers:
LC = 1 MSD − 1 VSD

Screw Gauge:
LC = Pitch / Circular Scale Division

---

6. Concept Tree

Measurement → Instrument → Least Count → Precision → Comparison → MCQ → NEET Trick

---

7. Flow Chart

Measurement → Least Count → Smaller LC → Higher Precision → Correct Answer

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8. Common Mistakes

❌ Accuracy और Precision को एक समझ लेना
❌ Larger Least Count को ज्यादा Precision समझ लेना
❌ Formula भूल जाना

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9. NEET Trick

Question में सभी instruments की Least Count compare करो

✔ सबसे छोटा LC → Correct Answer

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10. PYQ Strategy

Step 1: Instrument पहचानो
Step 2: Least Count निकालो
Step 3: Compare करो
Step 4: Smallest LC चुनो

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11. One Page Revision

Measurement → Least Count → Accuracy → Precision → Vernier → Screw Gauge → Optical → Smallest LC = Best

---

12. 15 Second Revision

Least Count छोटा → Precision बड़ा → Optical Best → Answer (C)

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13. Sample MCQ

Q: सबसे अधिक precise instrument कौन है?

A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument

Answer: D

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14. Assertion Reason

Assertion: Optical instrument सबसे precise है
Reason: इसका least count सबसे कम है

Answer: Both true and correct explanation

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15. Final Memory Map

Measurement → Least Count → Precision → Comparison → Trick → MCQ → Revision

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Golden Formula

Smallest Least Count = Highest Precision = Correct Answer

NEET Practice Questions

Topic: Precision, Least Count, Measuring Instruments

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1. Direct MCQs (Single Correct Option)

Q1 (Easy)
Which instrument has the smallest least count?

A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument

Answer: D (Optical Instrument)

Q2 (Easy)
Least count is defined as:

A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement

Answer: B

Q3 (Moderate)
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:

A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm

Answer: C

Q4 (Hard)
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:

A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm

Answer: B

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2. Statement-Based Questions

Q5
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.

A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true

Answer: A

Q6
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.

A) Both true
B) I true II false
C) I false II true
D) Both false

Answer: B

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3. Assertion and Reason (A & R)

Q7
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.

A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true

Answer: A

Q8
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.

A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true

Answer: A

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4. Match the Columns

Q9
Match Column I with Column II:

Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument

Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm

Answer:
1 → B
2 → C
3 → D
4 → A

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5. Diagram / Graph-Based Questions

Q10
A graph shows comparison of least count of instruments:

Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)

Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise

Answer: C

Q11
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero

Answer: B

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Final NEET Shortcut Rule

✔ Least Count ↓ → Precision ↑
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision

NEET Practice Questions

Topic: Precision, Least Count, Measuring Instruments

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1. Direct MCQs (Single Correct Option)

Q1 (Easy)
Which instrument has the smallest least count?

A) Metre Scale
B) Vernier Callipers
C) Screw Gauge
D) Optical Instrument

Answer: D (Optical Instrument)

Q2 (Easy)
Least count is defined as:

A) Maximum measurement
B) Smallest measurable value
C) Average value
D) Error in measurement

Answer: B

Q3 (Moderate)
A screw gauge has pitch 1 mm and 100 divisions. Its least count is:

A) 1 mm
B) 0.1 mm
C) 0.01 mm
D) 0.001 mm

Answer: C

Q4 (Hard)
Vernier callipers has 20 VSD = 19 MSD. If 1 MSD = 1 mm, least count is:

A) 0.1 mm
B) 0.05 mm
C) 0.02 mm
D) 0.2 mm

Answer: B

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2. Statement-Based Questions

Q5
Statement I: Smaller least count means higher precision.
Statement II: Screw gauge is more precise than vernier callipers.

A) Both true and II explains I
B) Both true but II does not explain I
C) I true II false
D) I false II true

Answer: A

Q6
Statement I: Optical instruments can measure up to wavelength of light.
Statement II: They are less precise than screw gauge.

A) Both true
B) I true II false
C) I false II true
D) Both false

Answer: B

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3. Assertion and Reason (A & R)

Q7
Assertion (A): Screw gauge is more precise than vernier callipers.
Reason (R): It has smaller least count.

A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true

Answer: A

Q8
Assertion: Optical instrument is most precise measuring device.
Reason: Its least count is equal to wavelength of light.

A) Both true and correct explanation
B) Both true but not explanation
C) A true R false
D) A false R true

Answer: A

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4. Match the Columns

Q9
Match Column I with Column II:

Column I:
1. Metre Scale
2. Vernier Callipers
3. Screw Gauge
4. Optical Instrument

Column II:
A. 0.0005 mm
B. 1 mm
C. 0.05 mm
D. 0.01 mm

Answer:
1 → B
2 → C
3 → D
4 → A

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5. Diagram / Graph-Based Questions

Q10
A graph shows comparison of least count of instruments:

Metre Scale → ██████████ (1 mm)
Vernier Callipers → ████ (0.05 mm)
Screw Gauge → ██ (0.01 mm)
Optical Instrument → █ (0.0005 mm)

Which conclusion is correct? A) Metre scale most precise
B) Screw gauge least precise
C) Optical instrument most precise
D) Vernier is most precise

Answer: C

Q11
If least count decreases in a graph, precision: A) Decreases
B) Increases
C) Remains same
D) Becomes zero

Answer: B

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Final NEET Shortcut Rule

✔ Least Count ↓ → Precision ↑
✔ Smallest LC = Correct Answer
✔ Optical Instrument = Highest Precision

🔗 11. Internal Links

/neet-physics-measurement-basics

/least-count-vernier-callipers-explained

/screw-gauge-formula-and-examples

/optical-instruments-physics-neet

/physics-mcqs-class-11-chapter-1

/assertion-reason-questions-physics

/neet-short-tricks-physics