📏 Units & Quantities
Every measurement in engineering means nothing without its unit. Before any calculation, an engineer must know exactly what's being measured, in what unit, and to what precision.
2Topics
8Worked Examples
4Eng. Cases
12Practice Qs
📐SI Units & PrefixesBase units, kilo, milli, micro…
🔄Conversion & Sig FigsChanging units safely
⚙️ApplicationsReal engineering
🎮Quick-Fire GameTest your speed
📝PracticeGraded questions
🎯What you will learn
Identify the seven SI base units and common derived units; use SI prefixes to scale measurements up and down; convert between units confidently; and round answers to a sensible number of significant figures.
💡 An answer of "42" means nothing in engineering — "42 mm" does. Always carry units through every step of a calculation, not just at the end.
🧭How to use this resource
1. Read the rules banner at the top of each tab
2. Experiment with the interactive tool
3. Check the key vocabulary panel
4. Study the animated visual, then the worked examples
📐
SI Units & Prefixes
Seven base units, and a set of prefixes that scale them up or down by powers of ten.
🔧SI Prefix ConverterEnter a value and choose the prefix to convert to
Enter a value and choose the prefixes, then press Convert to see the powers-of-ten calculation…
📖 Key Vocabulary
SI base unit — one of seven fundamental measurement units that all other units are built from.
Derived unit — a unit formed by combining base units, e.g. m/s (speed), N (force).
Prefix — a multiplier attached to a unit, e.g. "kilo" means ×1000.
Order of magnitude — the power of ten that best describes a quantity's size.
👁️ Visual aid: the pulsing dot marks the unscaled base unit — every prefix simply multiplies or divides it by a power of ten.
✏️Worked Example 1 — Identifying base unitsType: Recognition
Question State the SI base unit for mass, length and time.
Recall Mass → kilogram (kg); Length → metre (m); Time → second (s)
Answer kg, m, s — three of the seven SI base units.
🔢Worked Example 2 — Applying a prefixType: Prefix scaling
Question Express 0.045 A using an appropriate prefix.
Convert
0.045 A = 45 × 10⁻³ AAnswer 45 mA (milliamps) — a much more natural way to state this current.
🏗️Worked Example 3 — Recognising a derived unitType: Derived units
Question Show that the Newton (N), the unit of force, is built from base units.
Recall Force = mass × acceleration; acceleration has units m/s²
Answer N = kg·m/s² — the Newton is entirely built from the base units kg, m and s.
⚙️Worked Example 4 — Engineering context (choosing sensible units)Type: Engineering
Question A workshop measures a shaft diameter as 0.0125 m and a cable length as 3200 m. Restate both using better-suited prefixes.
Shaft diameter
0.0125 m = 12.5 × 10⁻³ mCable length
3200 m = 3.2 × 10³ mAnswer Shaft diameter = 12.5 mm; cable length = 3.2 km — both far easier to read and communicate on a drawing or spec sheet.
🧠 Common slip: mixing up milli (10⁻³) and micro (10⁻⁶) — always double-check the prefix symbol (m vs μ) before converting, since they differ by a factor of 1000.
🔄
Unit Conversion & Significant Figures
Moving safely between units, and stating answers to a sensible level of precision.
🔧Unit ConverterConvert between common length, mass and time units
Enter a value and choose units, then press Convert to see the conversion factor applied…
📖 Key Vocabulary
Conversion factor — the fixed multiplier that relates one unit to another.
Significant figures (s.f.) — the digits in a number that carry genuine measurement precision.
Decimal places (d.p.) — the number of digits shown after the decimal point.
Rounding — reducing a number's precision to a sensible level, following the "round half up" convention.
👁️ Visual aid: the animated marker traces how the decimal point effectively shifts three places when converting between metres and millimetres.
✏️Worked Example 1 — Length conversionType: Basic conversion
Question Convert 3.2 m to mm.
Apply factor
1 m = 1000 mm, so 3.2 × 1000Answer 3.2 m = 3200 mm
⏱️Worked Example 2 — Time conversionType: Basic conversion
Question Convert 2.5 hours to minutes.
Apply factor
1 hour = 60 minutes, so 2.5 × 60Answer 2.5 hours = 150 minutes
🔢Worked Example 3 — Rounding to significant figuresType: Significant figures
Question Round 128.457 to 3 significant figures.
Identify first 3 sig figs
1, 2, 8 — the next digit (4) rounds downAnswer 128.457 ≈ 128 (3 s.f.)
⚙️Worked Example 4 — Engineering context (combined conversion)Type: Engineering
Question A component's mass is measured as 0.750 kg. State this in grams, and to 2 significant figures.
Convert
0.750 kg × 1000 = 750 gRound to 2 s.f.
750 → 750 (already 2 s.f. meaningful digits, trailing zero)Answer 750 g — a QC report might state this as "7.5 × 10² g" to make the 2 s.f. precision unambiguous.
🧠 Common slip: rounding too early in a multi-step calculation — this can introduce small errors that grow through later steps. Always round only the final answer.
⚙️
Engineering Applications
Four live scenarios — each with its own calculator. Enter your own numbers.
🔩 Component Drawing Tolerances
Engineering drawings often specify dimensions in mm; converting to/from metres is a routine daily task.
1 m = 1000 mm
📟 Try it — mm ↔ m Converter
Enter a value and direction, then press Calculate…
⚡ Electrical Current Scaling
Electronic components often specify current in mA or μA; converting to base amps avoids errors in circuit calculations.
1 A = 1000 mA = 1,000,000 μA
📟 Try it — Current Prefix Converter
Enter value and units, then press Calculate…
⏱️ Production Cycle Time
Converting between seconds, minutes and hours is essential for planning production line throughput.
1 hour = 3600 seconds
📟 Try it — Cycle Time Converter
Enter value and units, then press Calculate…
⚖️ Reporting Mass to the Right Precision
QC reports should state measured mass to a number of significant figures matching the scale's actual precision.
Round to n significant figures
📟 Try it — Significant Figure Rounder
Enter a value and number of sig figs, then press Calculate…
🎮
Quick-Fire Units & Quantities Game
12 questions on SI units, prefixes and conversion. How many can you get?
⚡ Units & Quantities Challenge
Score: 0Question: 1/12Streak: 0🔥
Press Start to begin!
📝
Practice Questions
Graded from warm-up to challenge. Attempt fully before revealing the working.
Question 1 🥉2 marks
State the SI base unit for time.
second (s)
Question 2 🥉2 marks
Convert 5 km to m.
5 × 1000 = 5000 m
Question 3 🥉2 marks
Convert 2500 g to kg.
2500 ÷ 1000 = 2.5 kg
Question 4 🥉2 marks
Round 47.283 to 2 significant figures.
47
Question 5 🥈3 marks
Convert 0.045 A to mA.
0.045 × 1000 = 45 mA
Question 6 🥈4 marks
A cable is 2.35 km long. State this in metres and in millimetres.
2.35 × 1000 = 2350 m
2350 × 1000 = 2,350,000 mm
2350 × 1000 = 2,350,000 mm
Question 7 🥈3 marks
Round 0.006284 to 2 significant figures.
First 2 sig figs: 6, 2 (leading zeros don't count)
0.0063
0.0063
Question 8 🥈4 marks
Show that the Watt (unit of power) equals kg·m²/s³, given power = force × velocity and force = kg·m/s².
Power = Force × velocity = (kg·m/s²) × (m/s)
= kg·m²/s³
= kg·m²/s³
Question 9 🥇4 marks
A machine cycle takes 90 seconds. Express this in minutes, and state how many cycles complete in an 8-hour shift.
90 ÷ 60 = 1.5 minutes
8 hours = 480 minutes; 480 ÷ 1.5 = 320 cycles
8 hours = 480 minutes; 480 ÷ 1.5 = 320 cycles
Question 10 🥇5 marks
A sensor reads 0.000825 A. Express this using the most appropriate SI prefix, and to 2 significant figures.
0.000825 A = 825 × 10⁻⁶ A = 825 μA
To 2 s.f.: 830 μA
To 2 s.f.: 830 μA
Question 11 🥇5 marks
A batch of 240 components takes 6 hours to produce. Find the average production rate in components per minute, to 3 significant figures.
6 hours = 360 minutes
240 ÷ 360 = 0.6667
≈ 0.667 components/min (3 s.f.)
240 ÷ 360 = 0.6667
≈ 0.667 components/min (3 s.f.)
Question 12 🥇5 marks
A force of 4500 N acts on a 0.25 m² area. Find the pressure in Pa (N/m²), and re-express it in kPa to 3 significant figures.
Pressure = 4500 ÷ 0.25 = 18000 Pa
18000 Pa = 18 kPa (already exact)
18.0 kPa (3 s.f.)
18000 Pa = 18 kPa (already exact)
18.0 kPa (3 s.f.)