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Practice On Finding The Zero Error Of A Vernier Caliper

Key idea: Practice finding vernier caliper zero error: 6 diagram questions with answers, sign convention reminders, and exam-friendly working for O Level Physics.

  • G3 Physics topic extensions
On this page

Learning objectives

  • Read an analogue vernier caliper scale and correct the reading for zero error

1. Definition

A. What you are practising

Assume the jaws are tightly closed. Find the zero error of each vernier caliper (in cm).

If you need a refresher, use: How To Use Calipers (Digital + Vernier) and Accuracy, Precision & Measurement Errors.

2. Key Ideas

  • Zero error is the reading shown when the jaws are closed.
  • Sign convention:
    • Positive zero error: vernier zero is to the right of main zero.
    • Negative zero error: vernier zero is to the left of main zero.

3. Detailed Explanations

A. Quick workflow

  1. Look at where the vernier zero is compared to the main zero.
  2. Find the aligned vernier division and convert it to cm.
  3. Decide the sign (left = negative, right = positive).

For a 10-division vernier with least count 0.01 cm:

  • zero to the right: error = +(aligned division) × 0.01 cm
  • zero to the left: error = -(10-aligned division) × 0.01 cm

4. Common Mistakes

A. Typical slips

  • Writing the right magnitude but wrong sign.
  • Using the wrong aligned line (choose the best alignment).
  • Forgetting the unit.

5. Exam Tips

A. One-line method statement

Write the sign first. For a positive error use the aligned division; for a negative error count the remaining divisions from the aligned mark to vernier 10.

5A. Interactive Zero-Error Trainer

Simulation Flow: Zero Error -> Correction -> Exam Practice

Run a few random zero-error cases here, then do the static question set below for exam-style consolidation.

Simulation Trainer: Vernier Zero Error + Correction

Use the top closed-jaws scale to find zero error, then correct the observed reading from the bottom scale.

BetaO LevelA LevelPractical SkillsBest for: O Level and H2 learners losing marks on correction sign
  • Zero-Error Sign
  • Zero-Error Magnitude
  • Corrected Reading

Open the full interactive simulation on its own page

Use the standalone simulation page for the live controls, SVG scene, run modes, and scoring flow.

Open Interactive Simulation

The lesson stays lightweight and links out to the dedicated simulation page.

After this trainer
  1. Measurement Quiz
  2. Structured Measurement
  3. Practice: Vernier Reading with Zero Error
  4. How To Use Calipers (Digital + Vernier)

6. Worked Examples

Modelled example 1

Question 1 — model a negative zero error

Core

Problem

The jaws are closed. Find the zero error in centimetres.
Vernier zero-error question 1Jaws closed: with the jaws closed, vernier zero lies to the left of main zero, and vernier division 4 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment
Study the worked solution

  1. Choose the sign

    Method

    The zero error is negative.

    Reason

    Vernier zero lies to the left of main zero.

    Working

    left offset ⇒ -

  2. Find the magnitude

    Method

    The magnitude is 0.06 cm.

    Reason

    Division 4 aligns, leaving 10-4 = 6 divisions to the vernier 10 mark.

    Working

    (10-4)(0.01) = 0.06 cm

  3. Combine sign and magnitude

    Method

    The zero error is -0.06 cm.

    Reason

    The left offset fixes the negative sign.

    Working

    e₀ = -0.06 cm

Guided practice 2

Question 2 — positive zero error

About 3 min

Problem

The jaws are closed. Find the zero error in centimetres.
Vernier zero-error question 2Jaws closed: with the jaws closed, vernier zero lies to the right of main zero, and vernier division 6 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment

Try this before viewing the solution

Unit: cm

Hints

Hint 1: sign before magnitude
Right of main zero means positive; then use aligned division 6.
View solution step by step

  1. Set the sign

    Method

    The error is positive.

    Reason

    Vernier zero is to the right of main zero.

    Working

    right offset ⇒ +

  2. Calculate

    Method

    The zero error is + 0.06 cm.

    Reason

    Aligned division 6 gives six least counts.

    Working

    e₀ = +6(0.01) = +0.06 cm

Guided practice 3

Question 3 — complementary count

About 4 min

Problem

The jaws are closed. Find the zero error in centimetres.
Vernier zero-error question 3Jaws closed: with the jaws closed, vernier zero lies to the left of main zero, and vernier division 6 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment

Try this before viewing the solution

Unit: cm

Hints

Hint 1: use the complement
For a left offset, the magnitude is (10-n)(0.01 cm).
View solution step by step

  1. Set the sign

    Method

    The error is negative because vernier zero is left of main zero.

    Reason

    The offset direction determines sign.

    Working

    e₀ < 0

  2. Find the complement

    Method

    Four divisions remain after aligned division 6.

    Reason

    10-6 = 4.

    Working

    (10-6)(0.01) = 0.04 cm

  3. State the result

    Method

    e₀ = -0.04 cm.

    Reason

    Combine the negative direction with the calculated magnitude.

    Working

    e₀ = -0.04 cm

Common misconception 4

Question 4 — sign misconception

Find and correct the mistake

Learner claim

A learner reports -0.03 cm because the instrument needs a correction. Diagnose the zero-error sign.
Vernier zero-error question 4Jaws closed: with the jaws closed, vernier zero lies to the right of main zero, and vernier division 3 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment

Try this before viewing the solution

Unit: cm

View solution step by step

  1. Distinguish error from correction

    Method

    The requested value is the instrument’s zero error, not the later correction.

    Reason

    Correction is subtracted from observed readings and therefore carries the opposite operation.

    Working

    x_correct = x_observed-e₀

  2. Read direction and magnitude

    Method

    Right offset and aligned division 3 give + 0.03 cm.

    Reason

    Right means positive and 3(0.01) = 0.03.

    Working

    e₀ = +3(0.01) = +0.03 cm

Examiner practice 5

Question 5 — examiner negative-error method

3 marks

Examination question

The jaws are closed. Determine the signed zero error and show the complementary-division method. [3 marks]
Vernier zero-error question 5Jaws closed: with the jaws closed, vernier zero lies to the left of main zero, and vernier division 7 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment

Try this before viewing the solution

Unit: cm

View solution step by step

  1. Sign

    1 mark

    Method

    The error is negative.

    Reason

    Vernier zero is left of main zero.

    Working

    e₀ < 0

  2. Magnitude

    1 mark

    Method

    The magnitude is 0.03 cm.

    Reason

    Three divisions remain from 7 to 10.

    Working

    (10-7)(0.01) = 0.03 cm

  3. Signed result

    1 mark

    Method

    e₀ = -0.03 cm.

    Reason

    Combine the negative direction and magnitude.

    Working

    e₀ = -0.03 cm

Challenge 6

Question 6 — boundary reading and correction direction

Minimal support

Independent transfer

The jaws are closed. Find the signed zero error, then state whether it must be added to or subtracted from future observed readings.
Vernier zero-error question 6Jaws closed: with the jaws closed, vernier zero lies to the right of main zero, and vernier division 10 aligns with a main-scale line.Jaws closedmain scale (cm)01vernier scale0510best alignment

Try this before viewing the solution

Unit: cm
Correction operation

Hints

Hint 1: separate error and correction
First read e₀; then use x_correct = x_observed-e₀.
View solution step by step

  1. Read the boundary case

    Method

    The zero error is + 0.10 cm.

    Reason

    Vernier zero is right of main zero and aligned division 10 represents ten least counts.

    Working

    e₀ = +10(0.01) = +0.10 cm

  2. Infer the correction

    Method

    Subtract 0.10 cm from future observed readings.

    Reason

    A positive zero error makes each observed reading too large by that amount.

    Working

    x_correct = x_observed-0.10 cm

7. Mind Stretchers

Mind stretcher 1: Apply the correction ruleExtension

A vernier caliper has zero error -0.04 cm. The observed reading of an object is 3.34 cm. Find the correct reading.

Show Answer

correct = 3.34 - (-0.04) = 3.38 cm

Mind stretcher 2: What type of error is zero error?Extension

Is zero error random or systematic? Explain briefly.

Show Answer

Zero error is systematic because it shifts every reading by the same amount (same direction).

Continue with the next resource in this course.

Course and syllabus information
Course
G3 Physics topic extensions
Syllabus scope
Beyond the syllabus
Edition
G3 Physics topic extensions