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Learn the conversion, then check the number. Work through SI prefixes, area, volume, density and standard form before they cost you a step in a Physics calculation.
Original practice from Dr Desouky Physics Academy. The examples are teaching exercises, not exam-board questions.
Choose matching units of the same quantity. Use a decimal or calculator notation such as 4.7e-6. The example starts with 250 cm = 2.5 m.
Use a dot for decimals and omit commas and unit symbols. Signed numbers are supported; whether a negative value makes physical sense depends on the quantity and context. This tool uses scale factors, so it does not convert temperatures.
Converted value
2.5 m
Standard form: 2.5 × 100 m
Conversion factor: 1 cm = 0.01 m.
Working: 250 × 0.01 ÷ 1 = 2.5 m. The factors convert through m.
Results show up to 10 significant digits, not the precision of a measurement. Keep extra digits during working and round your final answer to suit the data and question.
A prefix is a multiplier attached to the unit. For example, 1 mA means 10⁻³ A. Capital letters matter: mW is milliwatts, while MW is megawatts. This is a general reference; the prefixes required by your course depend on its specification.
Reference: NIST guide to SI prefixes.
For 350 mA, write 1 mA = 10⁻³ A, then calculate 350 × 10⁻³ = 0.350 A. When the target unit is larger, fewer of those units are needed for the same quantity. This provides a quick check on the direction of your conversion.
Since 1 cm = 10⁻² m, 1 cm² = 10⁻⁴ m² and 1 cm³ = 10⁻⁶ m³. The power acts on the prefix as well as the unit. Using 10⁻² for an area would make the answer 100 times too large. For example, 12 cm² = 0.0012 m².
For density, 1 g/cm³ = 10⁻³ kg ÷ 10⁻⁶ m³ = 10³ kg/m³. For speed, 1 km/h = 1000 m ÷ 3600 s. A denominator is part of the unit: changing only the numerator changes the physical value.
In F = ma, using kilograms and metres per second squared gives newtons. In ρ = m/V, using grams and cubic centimetres gives g/cm³. You can work consistently in either density unit, then convert if the question asks for a different one. Check the requested answer unit before starting.
The treatment of powered prefixes follows NIST’s rules for using units. The numerical exercises here are original.
Write a non-zero number as a × 10ⁿ, with 1 ≤ |a| < 10 and an integer power n. For example, 62,000 = 6.2 × 10⁴ and 0.00062 = 6.2 × 10⁻⁴. A small positive number has a negative exponent, not a negative value.
In calculator notation, 6.2e-4 means 6.2 × 10⁻⁴. Enter it as one number. If you type a longer expression, use brackets around the entire numerator or denominator where needed.
Standard form can preserve the stated precision: 3.0 × 10³ has two significant figures and 3.00 × 10³ has three. Leading zeros do not count. A converter may display both as 3000, so copy the precision required by the question, not just the digits shown by the tool. Exact unit-conversion factors do not introduce measurement uncertainty.
Try each on paper before opening the answer. Record whether a mistake came from the prefix, the power, the denominator or calculator entry.
20 m/s
72 × 1000 ÷ 3600 = 20. You change both kilometres to metres and hours to seconds; dividing by 3.6 combines the two steps.
2.50 × 10⁻⁴ m³
One centimetre is 10⁻² m, so one cubic centimetre is (10⁻²)³ = 10⁻⁶ m³. Multiply 250 by 10⁻⁶. The stated answer assumes the original value was given to three significant figures.
4.5 × 10⁻⁷ m²
The square applies to the unit conversion too: 1 mm² = (10⁻³ m)² = 10⁻⁶ m². Then 0.45 × 10⁻⁶ = 4.5 × 10⁻⁷.
2700 kg/m³
Convert the numerator and denominator: (2.7 × 10⁻³ kg) ÷ (10⁻⁶ m³) = 2.7 × 10³ kg/m³. The conversion factor is 1000, not 10⁻³.
4.7 × 10⁻⁶ F
Micro means 10⁻⁶. A microfarad is one millionth of a farad, so the numerical value becomes much smaller when expressed in farads.
3.2 A
Milli means 10⁻³. Multiply 3.2 × 10³ by 10⁻³; the powers cancel. Enter 3.2e3 in the calculator for the original value.
5.6 × 10⁻⁴ m = 560 μm
Move the decimal four places to make the coefficient 5.6. To express metres in micrometres, divide by 10⁻⁶: 0.00056 ÷ 10⁻⁶ = 560.
2.7 × 10⁶ J
1 kW = 1000 J/s and 1 h = 3600 s, so 1 kWh = 3.6 × 10⁶ J. Multiply this by 0.75. Kilowatt-hour is an energy unit; kilowatt is a power unit.
The Cambridge IGCSE Physics 0625 syllabus for 2026–2028 includes handling units and numerical data. For Edexcel International A-Level, check the current specification and its unit-prefix addendum. This practice supports calculation skills; it is not a full syllabus checklist.
Identify the step you missed, try a fresh question, and return to it in a later session. Use the free Physics revision planner to make room for regular practice. For help applying these skills to your course, explore IGCSE Physics tutoring or A-Level Physics tutoring.
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