An Instrument That Reads to Two Decimal Places and Still Lies to You
Learn to calculate the least count of a vernier calliper and a screw gauge, take a full reading from the main and auxiliary scales, identify and correct positive and negative zero error, and choose the right instrument.
Why can an instrument reading 3.45 mm still give the wrong answer?
A screw gauge reads to hundredths of a millimetre. Close its jaws on a wire, read mm, and it looks like a precise answer.
Now close the jaws on nothing at all, with no wire between them. If the reading is not zero — say the circular scale shows divisions — then the instrument is **already reading mm too high before you start**, and every measurement it gives is mm too big.
The wire is not mm. It is
This is a zero error, and it has a feature worth understanding: it shifts every reading by the same amount in the same direction. Repeating the measurement ten times and averaging will not remove it, because all ten readings are wrong identically. Only checking the closed instrument and subtracting will.
So two separate things decide how good a measurement is. The least count says how finely the instrument can read, and the zero error says whether that fine reading is honest. A fine instrument with an uncorrected zero error is worse than a coarse one without.
This page covers the second part of the ICSE Class 9 Physics chapter on measurements — least count, taking readings, correcting zero error, and choosing between the two instruments.
Now close the jaws on nothing at all, with no wire between them. If the reading is not zero — say the circular scale shows divisions — then the instrument is **already reading mm too high before you start**, and every measurement it gives is mm too big.
The wire is not mm. It is
This is a zero error, and it has a feature worth understanding: it shifts every reading by the same amount in the same direction. Repeating the measurement ten times and averaging will not remove it, because all ten readings are wrong identically. Only checking the closed instrument and subtracting will.
So two separate things decide how good a measurement is. The least count says how finely the instrument can read, and the zero error says whether that fine reading is honest. A fine instrument with an uncorrected zero error is worse than a coarse one without.
This page covers the second part of the ICSE Class 9 Physics chapter on measurements — least count, taking readings, correcting zero error, and choosing between the two instruments.
Formula
How do you calculate the least count of a vernier calliper?
Divide one main scale division by the number of divisions on the vernier scale:
Equivalently, , because the vernier scale is deliberately made slightly shorter per division than the main scale.
Why the two forms agree. In the standard instrument, vernier divisions are made exactly as long as main divisions. So one vernier division is of a main division, and
which is as the first formula says. That tiny mismatch per division is the entire principle of the vernier, and it is why exactly one vernier division ever lines up with a main-scale mark.
Worked example 1 — the standard calliper. mm and there are vernier divisions:
Worked example 2 — a finer vernier. mm with vernier divisions:
Worked example 3 — a half-millimetre main scale. mm with vernier divisions:
Now the screw gauge. Here the fine motion comes from a screw thread, and two numbers are needed. The pitch is the distance the spindle advances in one complete rotation:
Worked example 4 — finding the pitch. The spindle moves mm in complete rotations:
Worked example 5 — least count of a screw gauge. Pitch mm with circular divisions:
Worked example 6 — the same least count from different numbers. Pitch mm with circular divisions:
So the same fineness can be reached two ways, and the least count must be computed from the actual instrument rather than assumed.
The pitch is per COMPLETE rotation. If the spindle moves mm in turns, the pitch is mm and not mm — and using the total distance as the pitch makes every subsequent reading four times too large. Always divide by the number of turns, and write that division out.
Equivalently, , because the vernier scale is deliberately made slightly shorter per division than the main scale.
Why the two forms agree. In the standard instrument, vernier divisions are made exactly as long as main divisions. So one vernier division is of a main division, and
which is as the first formula says. That tiny mismatch per division is the entire principle of the vernier, and it is why exactly one vernier division ever lines up with a main-scale mark.
Worked example 1 — the standard calliper. mm and there are vernier divisions:
Worked example 2 — a finer vernier. mm with vernier divisions:
Worked example 3 — a half-millimetre main scale. mm with vernier divisions:
Now the screw gauge. Here the fine motion comes from a screw thread, and two numbers are needed. The pitch is the distance the spindle advances in one complete rotation:
Worked example 4 — finding the pitch. The spindle moves mm in complete rotations:
Worked example 5 — least count of a screw gauge. Pitch mm with circular divisions:
Worked example 6 — the same least count from different numbers. Pitch mm with circular divisions:
So the same fineness can be reached two ways, and the least count must be computed from the actual instrument rather than assumed.
The pitch is per COMPLETE rotation. If the spindle moves mm in turns, the pitch is mm and not mm — and using the total distance as the pitch makes every subsequent reading four times too large. Always divide by the number of turns, and write that division out.
How do you take a full reading from both scales?
Read the main scale just before the auxiliary scale's zero, then add the coinciding division multiplied by the least count:
For a vernier calliper, the coinciding division is the one vernier mark that lines up exactly with any main-scale mark.
Worked example 1. cm. The vernier zero lies just past the cm mark, and the th vernier division coincides:
Worked example 2. cm, cm, and the th division coincides:
Worked example 3 — in millimetres. mm, mm, th division coinciding:
For a screw gauge, the main scale runs along the sleeve and the circular scale is on the rotating thimble:
Worked example 4. mm, sleeve shows mm, circular scale reads :
Worked example 5. mm, sleeve mm, circular scale :
Worked example 6 — a half-millimetre sleeve. Pitch mm with divisions, so mm. The sleeve shows mm and the half-millimetre mark past it, with the circular scale reading :
The half-millimetre mark is easy to miss and costs exactly mm when it is — which is fifty times the least count, so the instrument's fineness is wasted by a reading error far larger than its precision.
Only one vernier division can coincide. Because each vernier division is shorter than a main division by the least count, the marks drift out of alignment on both sides of the coinciding one. If two seem to line up, look again with better light — and if the answer is genuinely between two, the digit is uncertain and should be reported as such.
Write the number of decimal places the least count justifies. A vernier with cm gives cm — two decimal places in centimetres. **Writing cm claims a precision the instrument does not have**, and writing cm throws away precision it does. The least count decides the format of the answer, not the neatness of the number.
For a vernier calliper, the coinciding division is the one vernier mark that lines up exactly with any main-scale mark.
Worked example 1. cm. The vernier zero lies just past the cm mark, and the th vernier division coincides:
Worked example 2. cm, cm, and the th division coincides:
Worked example 3 — in millimetres. mm, mm, th division coinciding:
For a screw gauge, the main scale runs along the sleeve and the circular scale is on the rotating thimble:
Worked example 4. mm, sleeve shows mm, circular scale reads :
Worked example 5. mm, sleeve mm, circular scale :
Worked example 6 — a half-millimetre sleeve. Pitch mm with divisions, so mm. The sleeve shows mm and the half-millimetre mark past it, with the circular scale reading :
The half-millimetre mark is easy to miss and costs exactly mm when it is — which is fifty times the least count, so the instrument's fineness is wasted by a reading error far larger than its precision.
Only one vernier division can coincide. Because each vernier division is shorter than a main division by the least count, the marks drift out of alignment on both sides of the coinciding one. If two seem to line up, look again with better light — and if the answer is genuinely between two, the digit is uncertain and should be reported as such.
Write the number of decimal places the least count justifies. A vernier with cm gives cm — two decimal places in centimetres. **Writing cm claims a precision the instrument does not have**, and writing cm throws away precision it does. The least count decides the format of the answer, not the neatness of the number.
How do you identify and correct a zero error?
Close the instrument on nothing and read it. If the reading is not zero, that value is the zero error, and
taking the error with its sign. That one sentence handles both cases.
Positive zero error — the auxiliary zero has gone past the main zero. The instrument reads high, so the error is positive and is subtracted.
Worked example 1 — vernier, positive error. With the jaws closed, the vernier zero lies to the right of the main zero and the rd division coincides. With cm:
An observed reading of cm corrects to
Negative zero error — the auxiliary zero has not reached the main zero. The instrument reads low, the error is negative, and subtracting a negative adds.
Worked example 2 — vernier, negative error. With the jaws closed the vernier zero lies to the left of the main zero, and the th division coincides on a scale of divisions. Count backwards from the total:
An observed reading of cm corrects to
Worked example 3 — screw gauge, positive error. With the jaws touching, the circular scale reads and mm:
An observed mm corrects to mm.
Worked example 4 — screw gauge, negative error. With the jaws touching, the circular scale reads on a scale of :
An observed mm corrects to mm.
Why the negative case counts backwards. A circular scale reading of does not mean the zero has advanced by divisions; it means it has fallen short by the divisions remaining to complete the turn. So the size of a negative error is the number of divisions still to go, and reading it as rather than turns a mm correction into a mm one.
Worked example 5 — the whole procedure. A wire is measured with a screw gauge of pitch mm and circular divisions, so mm. Closed, the circular scale reads — short of by , so the error is mm. On the wire, the sleeve shows mm and the circular scale reads :
A zero error is a SYSTEMATIC error, and averaging cannot touch it. Ten repeats of the wire measurement all give mm, and their average is mm — still wrong by mm. Random errors shrink on averaging and systematic ones do not, which is why the closed-instrument check is a required step and not a refinement. Recording the zero reading before any measurement is the habit that makes the correction possible at all, because once the instrument is put away the error cannot be recovered.
taking the error with its sign. That one sentence handles both cases.
Positive zero error — the auxiliary zero has gone past the main zero. The instrument reads high, so the error is positive and is subtracted.
Worked example 1 — vernier, positive error. With the jaws closed, the vernier zero lies to the right of the main zero and the rd division coincides. With cm:
An observed reading of cm corrects to
Negative zero error — the auxiliary zero has not reached the main zero. The instrument reads low, the error is negative, and subtracting a negative adds.
Worked example 2 — vernier, negative error. With the jaws closed the vernier zero lies to the left of the main zero, and the th division coincides on a scale of divisions. Count backwards from the total:
An observed reading of cm corrects to
Worked example 3 — screw gauge, positive error. With the jaws touching, the circular scale reads and mm:
An observed mm corrects to mm.
Worked example 4 — screw gauge, negative error. With the jaws touching, the circular scale reads on a scale of :
An observed mm corrects to mm.
Why the negative case counts backwards. A circular scale reading of does not mean the zero has advanced by divisions; it means it has fallen short by the divisions remaining to complete the turn. So the size of a negative error is the number of divisions still to go, and reading it as rather than turns a mm correction into a mm one.
Worked example 5 — the whole procedure. A wire is measured with a screw gauge of pitch mm and circular divisions, so mm. Closed, the circular scale reads — short of by , so the error is mm. On the wire, the sleeve shows mm and the circular scale reads :
A zero error is a SYSTEMATIC error, and averaging cannot touch it. Ten repeats of the wire measurement all give mm, and their average is mm — still wrong by mm. Random errors shrink on averaging and systematic ones do not, which is why the closed-instrument check is a required step and not a refinement. Recording the zero reading before any measurement is the habit that makes the correction possible at all, because once the instrument is put away the error cannot be recovered.
Which instrument should you use for which measurement?
Use the vernier calliper for lengths and diameters of a few centimetres, and the screw gauge for anything under a few millimetres where a tenth of a millimetre is too coarse.
What each is built like.
- A vernier calliper has two pairs of jaws — outside jaws for external measurements, inside jaws for internal ones — plus a depth strip, on a main scale usually reading in centimetres with a sliding vernier scale
- A screw gauge has a U-shaped frame with a fixed stud and a moving spindle driven by a fine screw, a sleeve carrying the main scale and a rotating thimble carrying the circular scale, and a ratchet at the end
What each can reach. A typical vernier calliper has cm, which is mm. A typical screw gauge has mm — ten times finer. But the screw gauge's range is only a couple of centimetres, while the calliper measures across its whole main scale.
So the choice is a trade between range and fineness, and the question to ask is whether the object is small enough to need the finer instrument and small enough to fit in it.
Worked choices.
- Diameter of a test tube — vernier calliper, using the outside jaws. Too large for a screw gauge
- Internal diameter of a pipe — vernier calliper, using the inside jaws. A screw gauge cannot reach inside anything
- Depth of a beaker — vernier calliper, using the depth strip
- Diameter of a thin wire — screw gauge. At mm, a calliper reading to mm would give only one meaningful digit
- Thickness of a sheet of paper or a glass slide — screw gauge
- Length of a pencil — an ordinary metre rule. A calliper would be pointless precision on a cm object measured to the nearest millimetre
The ratchet is not decoration. Turning the thimble directly lets you squeeze the object and read a thickness smaller than the truth, or strain the screw thread. The ratchet slips once a standard gentle pressure is reached, so every measurement is taken at the same grip — which makes readings comparable between people and between days.
Worked example — why fineness must match the object. A wire of true diameter mm measured with a calliper of mm reads mm, an uncertainty of roughly a quarter of the whole value. The same wire on a screw gauge of mm reads mm, an uncertainty of about one part in forty. Choosing the instrument is part of designing the measurement, not an afterthought once the object is in hand.
And fineness is wasted without the zero check. The screw gauge above gives mm to a hundredth of a millimetre, and an uncorrected zero error of mm makes that digit meaningless — a worse answer than the honest mm from the calliper. So the two halves of this page belong together: choose the instrument whose least count suits the object, then check its zero before trusting a single reading from it.
What each is built like.
- A vernier calliper has two pairs of jaws — outside jaws for external measurements, inside jaws for internal ones — plus a depth strip, on a main scale usually reading in centimetres with a sliding vernier scale
- A screw gauge has a U-shaped frame with a fixed stud and a moving spindle driven by a fine screw, a sleeve carrying the main scale and a rotating thimble carrying the circular scale, and a ratchet at the end
What each can reach. A typical vernier calliper has cm, which is mm. A typical screw gauge has mm — ten times finer. But the screw gauge's range is only a couple of centimetres, while the calliper measures across its whole main scale.
So the choice is a trade between range and fineness, and the question to ask is whether the object is small enough to need the finer instrument and small enough to fit in it.
Worked choices.
- Diameter of a test tube — vernier calliper, using the outside jaws. Too large for a screw gauge
- Internal diameter of a pipe — vernier calliper, using the inside jaws. A screw gauge cannot reach inside anything
- Depth of a beaker — vernier calliper, using the depth strip
- Diameter of a thin wire — screw gauge. At mm, a calliper reading to mm would give only one meaningful digit
- Thickness of a sheet of paper or a glass slide — screw gauge
- Length of a pencil — an ordinary metre rule. A calliper would be pointless precision on a cm object measured to the nearest millimetre
The ratchet is not decoration. Turning the thimble directly lets you squeeze the object and read a thickness smaller than the truth, or strain the screw thread. The ratchet slips once a standard gentle pressure is reached, so every measurement is taken at the same grip — which makes readings comparable between people and between days.
Worked example — why fineness must match the object. A wire of true diameter mm measured with a calliper of mm reads mm, an uncertainty of roughly a quarter of the whole value. The same wire on a screw gauge of mm reads mm, an uncertainty of about one part in forty. Choosing the instrument is part of designing the measurement, not an afterthought once the object is in hand.
And fineness is wasted without the zero check. The screw gauge above gives mm to a hundredth of a millimetre, and an uncorrected zero error of mm makes that digit meaningless — a worse answer than the honest mm from the calliper. So the two halves of this page belong together: choose the instrument whose least count suits the object, then check its zero before trusting a single reading from it.
Exam tip
Exam tip: compute the least count first and check the zero before anything
Write the least count on its own line before any reading. Show the division: or .
The pitch is per COMPLETE rotation. mm in turns gives a pitch of mm, not mm.
**Total reading MSR (coinciding division LC). Never add the division number itself.
Watch for the half-millimetre mark** on a screw gauge sleeve — missing it costs mm, fifty times the least count.
**True reading observed reading zero error, with its sign. One rule for both cases.
A positive error is subtracted; a negative error is added, since subtracting a negative adds.
For a negative error, count BACKWARDS to the end of the scale.** A circular scale reading out of gives mm, not mm.
Give the answer to the decimal places the least count justifies — cm for cm, neither nor .
Averaging removes random error, never zero error — say so when a question asks why the zero must be checked.
Match the instrument to the object: calliper for centimetres and for internal diameters and depths; screw gauge for wires and sheets; a metre rule for a pencil.
And mention the ratchet when asked how a screw gauge avoids over-tightening — it fixes the grip so readings are comparable.
The pitch is per COMPLETE rotation. mm in turns gives a pitch of mm, not mm.
**Total reading MSR (coinciding division LC). Never add the division number itself.
Watch for the half-millimetre mark** on a screw gauge sleeve — missing it costs mm, fifty times the least count.
**True reading observed reading zero error, with its sign. One rule for both cases.
A positive error is subtracted; a negative error is added, since subtracting a negative adds.
For a negative error, count BACKWARDS to the end of the scale.** A circular scale reading out of gives mm, not mm.
Give the answer to the decimal places the least count justifies — cm for cm, neither nor .
Averaging removes random error, never zero error — say so when a question asks why the zero must be checked.
Match the instrument to the object: calliper for centimetres and for internal diameters and depths; screw gauge for wires and sheets; a metre rule for a pencil.
And mention the ratchet when asked how a screw gauge avoids over-tightening — it fixes the grip so readings are comparable.
Did you know
Why a shorter division makes a finer instrument
The vernier scale works by being slightly wrong on purpose.
Take the standard calliper. Ten vernier divisions are made exactly as long as nine main divisions, so each vernier division is mm where each main division is mm. Every vernier mark therefore falls mm behind where the main scale would put it — the first by mm, the second by mm, the third by mm, and so on.
Now slide the vernier so its zero sits mm past a main mark. Which vernier division lines up?
The sixth. It had drifted back by exactly mm, and sliding forward by mm cancels that drift precisely. Every other division is still out of step. So the number of the coinciding division tells you the fraction of a millimetre directly — that is why the reading procedure is add the division number times the least count and nothing more.
It also explains why exactly one division can coincide. The drifts are , , mm and so on, all different, so only one of them can be cancelled by a given displacement.
The consequence is that a finer instrument needs a worse match between the scales. A -division vernier makes divisions equal to main ones, so each is out by mm and the least count halves. Push to divisions against and the least count becomes mm.
There is a limit, and it is not mathematical. The marks get closer together until the eye cannot tell which one coincides, and past that point more divisions add no information. The screw gauge sidesteps the problem entirely by converting a small straight movement into a large rotation, so its fine divisions are spread around a thimble with plenty of room — which is how it reaches ten times the fineness with marks you can still see.
Take the standard calliper. Ten vernier divisions are made exactly as long as nine main divisions, so each vernier division is mm where each main division is mm. Every vernier mark therefore falls mm behind where the main scale would put it — the first by mm, the second by mm, the third by mm, and so on.
Now slide the vernier so its zero sits mm past a main mark. Which vernier division lines up?
The sixth. It had drifted back by exactly mm, and sliding forward by mm cancels that drift precisely. Every other division is still out of step. So the number of the coinciding division tells you the fraction of a millimetre directly — that is why the reading procedure is add the division number times the least count and nothing more.
It also explains why exactly one division can coincide. The drifts are , , mm and so on, all different, so only one of them can be cancelled by a given displacement.
The consequence is that a finer instrument needs a worse match between the scales. A -division vernier makes divisions equal to main ones, so each is out by mm and the least count halves. Push to divisions against and the least count becomes mm.
There is a limit, and it is not mathematical. The marks get closer together until the eye cannot tell which one coincides, and past that point more divisions add no information. The screw gauge sidesteps the problem entirely by converting a small straight movement into a large rotation, so its fine divisions are spread around a thimble with plenty of room — which is how it reaches ten times the fineness with marks you can still see.
Exam relevance
Why does JEE Main keep returning to least count and zero error?
Because least count is the source of the uncertainty in every measurement, and the Class 11 chapter on errors is built directly on it.
This is the foundation for Class 11 Physics Units and Measurements, examined in JEE Main and NEET. The least count becomes the absolute error in a single reading, and from it come the relative error and the percentage error:
The worked comparison on this page — a mm wire measured to mm against mm — is a percentage-error calculation in everything but name, and it is the reason instrument choice matters.
Error propagation is the main new idea. Class 11 shows how errors combine: for a product or a quotient the relative errors add, and for a power the relative error is multiplied by that power. So the density of a sphere found from a screw-gauge diameter carries three times the relative error of the diameter, because volume depends on the cube of the radius. Questions of exactly that shape are a recurring JEE Main type, and they begin with the least count of the instrument named in the question.
Significant figures follow from the same source. A reading of cm has three significant figures because the least count justifies two decimal places, and Class 11 sets rules for how many survive a calculation. Reporting more digits than the least count allows is a marked error there, exactly as it is here.
The systematic-versus-random distinction is named and examined in Class 11. Zero error is the standard example of a systematic error, and the point made on this page — that averaging cannot remove it — is the standard assertion-reason item.
Where the instruments themselves appear. Vernier and screw-gauge readings are asked directly in JEE Main as numerical questions: given the least count, a main-scale reading, a coinciding division and a zero error, find the true value. Every step of that question is on this page, and the marks turn on the sign of the correction.
What the questions look like. For board work, expect calculate the least count from scale details or from pitch and divisions, find a total reading, apply a positive or negative zero-error correction, and compare the two instruments and choose one for a stated object. For JEE Main and NEET, expect a numerical reading with a zero error, and percentage-error or error-propagation questions built on a least count.
How board and competitive emphasis differ. A board paper rewards the written least-count calculation and a description of the instrument. A competitive paper gives the numbers and tests only whether the arithmetic and the sign come out right — usually as a single-answer numerical.
The single trap that costs the most marks. Getting the negative zero error the wrong way round. A circular scale reading out of with the jaws closed means the error is mm, so the correction adds mm — and reading it as mm, or subtracting instead of adding, gives a confidently wrong answer of the right general size. The defence is to write the single rule every time: true observed error, then substitute the error with its sign rather than reasoning about direction in your head.
This is the foundation for Class 11 Physics Units and Measurements, examined in JEE Main and NEET. The least count becomes the absolute error in a single reading, and from it come the relative error and the percentage error:
The worked comparison on this page — a mm wire measured to mm against mm — is a percentage-error calculation in everything but name, and it is the reason instrument choice matters.
Error propagation is the main new idea. Class 11 shows how errors combine: for a product or a quotient the relative errors add, and for a power the relative error is multiplied by that power. So the density of a sphere found from a screw-gauge diameter carries three times the relative error of the diameter, because volume depends on the cube of the radius. Questions of exactly that shape are a recurring JEE Main type, and they begin with the least count of the instrument named in the question.
Significant figures follow from the same source. A reading of cm has three significant figures because the least count justifies two decimal places, and Class 11 sets rules for how many survive a calculation. Reporting more digits than the least count allows is a marked error there, exactly as it is here.
The systematic-versus-random distinction is named and examined in Class 11. Zero error is the standard example of a systematic error, and the point made on this page — that averaging cannot remove it — is the standard assertion-reason item.
Where the instruments themselves appear. Vernier and screw-gauge readings are asked directly in JEE Main as numerical questions: given the least count, a main-scale reading, a coinciding division and a zero error, find the true value. Every step of that question is on this page, and the marks turn on the sign of the correction.
What the questions look like. For board work, expect calculate the least count from scale details or from pitch and divisions, find a total reading, apply a positive or negative zero-error correction, and compare the two instruments and choose one for a stated object. For JEE Main and NEET, expect a numerical reading with a zero error, and percentage-error or error-propagation questions built on a least count.
How board and competitive emphasis differ. A board paper rewards the written least-count calculation and a description of the instrument. A competitive paper gives the numbers and tests only whether the arithmetic and the sign come out right — usually as a single-answer numerical.
The single trap that costs the most marks. Getting the negative zero error the wrong way round. A circular scale reading out of with the jaws closed means the error is mm, so the correction adds mm — and reading it as mm, or subtracting instead of adding, gives a confidently wrong answer of the right general size. The defence is to write the single rule every time: true observed error, then substitute the error with its sign rather than reasoning about direction in your head.
Key takeaways
Least count, readings and zero error: quick revision
- Vernier least count .
- vernier divisions are made equal to main ones, so each is MSD and the difference is MSD.
- mm main scale with VSD gives ; with VSD, mm; a mm scale with VSD gives mm.
- Screw gauge: , and .
- mm in turns gives pitch mm — per complete rotation, not the total.
- Pitch mm with divisions gives mm; pitch mm with divisions gives the same mm.
- **Total reading MSR (coinciding division LC).**
- cm with the th division coinciding and cm gives cm; cm with the th gives cm; mm with the th at mm gives mm.
- Screw gauge: mm sleeve with CSR gives mm; mm with CSR gives mm.
- Watch the half-millimetre mark: mm mm. Missing it costs mm.
- Only one vernier division can coincide, because the drifts mm are all different.
- Report the decimal places the least count justifies — cm, not or .
- **True reading observed reading zero error, taking the error with its sign.
- Positive error (auxiliary zero past the main zero) is subtracted**: cm turns into cm; mm turns into mm.
- Negative error (auxiliary zero short of the main zero) is added: the th of gives cm, so becomes cm; of gives mm, so becomes mm.
- For a negative error, count backwards to the end of the scale — out of means divisions short.
- Full procedure: closed reading of gives mm; observed mm gives a true mm.
- Zero error is systematic, so averaging cannot remove it — ten repeats give the same wrong value.
- Vernier: outside jaws, inside jaws and a depth strip, about cm, wide range. Screw gauge: about mm, ten times finer, short range, with a ratchet fixing the grip.
- Choose by object: calliper for a test tube, a pipe's internal diameter or a beaker's depth; screw gauge for a wire or a sheet; a metre rule for a pencil.
- A mm wire read to mm is uncertain by a quarter of its value; read to mm, by about one part in forty.
Borrow a calliper from your lab, close it on nothing and write down what it reads — then measure the same object before and after correcting for that reading.
- vernier divisions are made equal to main ones, so each is MSD and the difference is MSD.
- mm main scale with VSD gives ; with VSD, mm; a mm scale with VSD gives mm.
- Screw gauge: , and .
- mm in turns gives pitch mm — per complete rotation, not the total.
- Pitch mm with divisions gives mm; pitch mm with divisions gives the same mm.
- **Total reading MSR (coinciding division LC).**
- cm with the th division coinciding and cm gives cm; cm with the th gives cm; mm with the th at mm gives mm.
- Screw gauge: mm sleeve with CSR gives mm; mm with CSR gives mm.
- Watch the half-millimetre mark: mm mm. Missing it costs mm.
- Only one vernier division can coincide, because the drifts mm are all different.
- Report the decimal places the least count justifies — cm, not or .
- **True reading observed reading zero error, taking the error with its sign.
- Positive error (auxiliary zero past the main zero) is subtracted**: cm turns into cm; mm turns into mm.
- Negative error (auxiliary zero short of the main zero) is added: the th of gives cm, so becomes cm; of gives mm, so becomes mm.
- For a negative error, count backwards to the end of the scale — out of means divisions short.
- Full procedure: closed reading of gives mm; observed mm gives a true mm.
- Zero error is systematic, so averaging cannot remove it — ten repeats give the same wrong value.
- Vernier: outside jaws, inside jaws and a depth strip, about cm, wide range. Screw gauge: about mm, ten times finer, short range, with a ratchet fixing the grip.
- Choose by object: calliper for a test tube, a pipe's internal diameter or a beaker's depth; screw gauge for a wire or a sheet; a metre rule for a pencil.
- A mm wire read to mm is uncertain by a quarter of its value; read to mm, by about one part in forty.
Borrow a calliper from your lab, close it on nothing and write down what it reads — then measure the same object before and after correcting for that reading.