Choosing measuring instruments and measuring length

1. Definitions

Range is the interval of values an instrument can measure. Resolution is the smallest change in reading it displays or distinguishes. A suitable instrument must cover the expected range and resolve the change that matters.

2. Key Ideas

Choosing an instrument

Length is measured in metres, although centimetres and millimetres are often more convenient in practical work. Choose an instrument by:

1. range — it must cover the whole measurement;
2. required precision — repeated readings must agree closely enough for the task;
3. resolution — the smallest scale division or displayed increment must be fine enough;
4. shape and access — for example, internal diameter or depth needs suitable caliper jaws or a depth rod.

Finer resolution supports a more precise reading, but it does not by itself guarantee accurate or repeatable results.

Always use the scale or display information supplied in the question if it differs from a typical value.

Choosing instruments for other physical quantities

The same decision works beyond length: first check that the instrument can cover the expected value, then decide whether its resolution is fine enough for the change you need to detect.

For a derived quantity, choose instruments for every measurement in its equation. To determine density, for example, you need mass and volume. A precise mass reading cannot rescue a poor volume measurement, so compare the likely percentage uncertainty of both.

3. Detailed Explanations

Correct measurement technique

Use the instrument-specific checks below after confirming that the instrument’s range and resolution suit the task.

Tape or rule

• Place the scale alongside and parallel to the length.
• Align one end with an intact zero mark.
• Read with the eye directly above the mark to avoid parallax.
• If the zero end is damaged, record two scale readings and subtract them.

Digital caliper

• Clean and close the jaws, then check or set zero.
• Use the correct jaws or depth rod.
• Hold the object gently and square to the jaws.
• Record the complete display with its unit.

Digital micrometer

• Check the zero before use.
• Place the object between anvil and spindle.
• Use the ratchet or specified constant-force control; do not overtighten.
• Record the complete display with its unit.

Improving small-length measurements

If one item is too thin for a rule, measure a larger total. For example, stack many sheets of paper, measure the stack, then divide by the number of sheets. Ensure the sheets are compressed consistently and count them correctly.

Repeat measurements at different positions when the object may not be uniform, such as the diameter of a wire or sphere. Calculate a mean if appropriate.

4. Common Mistakes

• Choosing the instrument with the smallest scale division without checking that its range fits the object.
• Reading a scale from an angle, which introduces parallax, or measuring from a worn end instead of a labelled mark.
• Reporting more decimal places than the instrument can justify.

5. Exam Tips

• State both why the range is suitable and why the resolution is sufficient.
• Align the object and scale, view normally, repeat the reading and describe how repeats will be combined.
• For a small repeated length such as paper thickness, measure many layers and divide by the counted number.

6. Worked Examples

Further mistakes to diagnose

• Choosing an instrument only because the object is “small”, without comparing required precision.
• Letting a tape sag or placing a rule at an angle to the measured length.
• Reading a scale from the side.
• Dropping meaningful zeros from a displayed or scale reading.
• Forgetting to zero digital calipers or micrometers.
• Overtightening a micrometer and deforming the object.

7. Mind Stretchers