Learn · Physics · Class 9

Physical Quantities & Measurement

Every measurement is a number AND a unit, and getting either wrong makes the whole answer wrong.

8 parts
Scroll to begin ↓
📘 DefinitionWhat physics measuresPart 1 of 8
🧩 The partsScalars and vectorsPart 2 of 8
🧮 EquationsPrefixes and standard formPart 3 of 8
✏️ Worked exampleMeasuring well, and estimating errorPart 4 of 8
🌍 In the real worldWhy units end careersPart 5 of 8
⚠️ Common mistakesWhere marks get lostPart 6 of 8
✅ SummaryWhat to rememberPart 7 of 8
✏️ Worked exampleWatch one worked throughPart 8 of 8
1📘 DefinitionPart 1 / 8

What physics measures

A physical quantity is anything that can be measured, length, time, mass, current. Every one is written as a number and a unit, and both are part of the answer. "5" is not a length; "5 m" is.

Physics separates quantities into two kinds:

  • Base quantities, the seven independent ones, defined on their own: length (m), mass (kg), time (s), current (A), temperature (K), amount (mol), light intensity (cd).
  • Derived quantities, built by combining base ones. Speed is length ÷ time, so its unit is m/s.

Getting the unit right is not decoration. It is how you check a formula makes sense.

2🧩 The partsPart 2 / 8

Scalars and vectors

The second split matters even more, because it changes how you add things up.

  • A scalar has size only: mass, time, speed, energy, distance.
  • A vector has size and direction: force, velocity, acceleration, displacement, momentum.

Walk 3 km east then 4 km north. Your distance is 7 km, scalars just add. Your displacement is 5 km north-east, because vectors add by direction too (3-4-5 triangle).

That is why a runner finishing a full lap has run 400 m but has a displacement of zero. Both statements are true and they are not contradictory.

3🧮 EquationsPart 3 / 8

Prefixes and standard form

Physics deals with the very large and very small, so numbers are written in standard form: a number between 1 and 10 times a power of ten.

0.0025 m = 2.5 × 10−3 m
45 000 m = 4.5 × 104 m

Prefixes do the same job more readably:

n nano 10−9 · µ micro 10−6 · m milli 10−3
k kilo 103 · M mega 106 · G giga 109

So 5 km = 5 × 103 m = 5000 m, and 3 mA = 3 × 10−3 A.

Always convert to base units before substituting into a formula. Mixing centimetres with metres is the single most common source of wrong answers in mechanics.

4✏️ Worked examplePart 4 / 8

Measuring well, and estimating error

Choosing the instrument. A metre rule reads to 1 mm. Vernier callipers read to 0.1 mm. A micrometer screw gauge reads to 0.01 mm. Use the one whose precision suits the object, callipers for a wire's diameter, a rule for a table.

Worked example. Measuring the thickness of one sheet of paper.

A single sheet is far thinner than a rule can resolve, so measure 500 sheets and divide.

500 sheets = 4.5 cm → 1 sheet = 4.5 ÷ 500 = 0.009 cm = 0.09 mm

The same trick times 20 oscillations of a pendulum rather than one: the reaction-time error is spread across 20 swings, so it matters 20 times less. That is the general principle, measure many, then divide.

5🌍 In the real worldPart 5 / 8

Why units end careers

In 1999 NASA lost the Mars Climate Orbiter (a spacecraft worth over $300 million) because one team supplied thrust data in pound-seconds while the navigation software expected newton-seconds. The number was right; the unit was not. The craft entered the atmosphere at the wrong altitude and was destroyed.

Closer to home, the same discipline runs everyday life: fuel sold in litres, cloth in metres, gold in grams, electricity billed in kilowatt-hours. A shopkeeper using an uncalibrated scale is committing a measurement error with a legal name.

Dimensional checking is the habit worth building. If you derive speed = distance × time, check the units: m × s is not m/s, so the formula is wrong, and you caught it before losing marks.

6⚠️ Common mistakesPart 6 / 8

Where marks get lost

  • Dropping the unit. A number alone earns no mark in physics.
  • Confusing mass and weight. Mass is in kg and does not change; weight is a force in newtons and depends on gravity. On the Moon your mass is the same, your weight is about one sixth.
  • Distance vs displacement, speed vs velocity. The first of each pair is scalar, the second vector.
  • Forgetting to convert. cm to m, g to kg, minutes to seconds. Do it before substituting.
  • Too many significant figures. If the data has 2 s.f. the answer cannot have 5.
7✅ SummaryPart 7 / 8

What to remember

  • Every quantity = number + unit.
  • Scalars size only · vectors size and direction.
  • Convert to base SI units before calculating.
  • Standard form and prefixes handle very large and very small values.
  • Measure many and divide to beat instrument and reaction error.
  • Mass ≠ weight.
8✏️ Worked examplePart 8 / 8

Watch one worked through

Here is one done slowly, with the reason for every move. Then one for you.

Watch one first

A student measures a wire as 2.5 cm with a ruler marked in millimetres. State the reading to the correct precision and give the absolute uncertainty.

  1. Identify the smallest division on the instrument.
    ruler smallest division = 1 mm = 0.1 cm
    Precision comes from the instrument, not from the number you happen to write. Always look at the scale first.
  2. Uncertainty is usually half the smallest division.
    ± 0.5 mm = ± 0.05 cm
    You can judge to half a division by eye. Claiming better than that from a plain ruler is not honest.
  3. Write the reading with its uncertainty and matching decimal places.
    2.50 ± 0.05 cm
    The value and its uncertainty must have the same number of decimal places, or the statement contradicts itself.
  4. Express it as a percentage if asked.
    (0.05 ÷ 2.50) × 100 = 2%
    Percentage uncertainty lets you compare measurements of different sizes, and it is what combines when quantities are multiplied.

Answer: 2.50 ± 0.05 cm, which is 2%

Now you try

A ruler has 1 mm divisions. What is the absolute uncertainty in mm?

Show the answer

0.5

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