What is the SI base unit of mass?

The kilogram (kg), not the gram.

Express the joule in SI base units.

kg m² s⁻² (energy = force × distance).

Express the watt in SI base units.

kg m² s⁻³ (power = energy ÷ time).

Express the pascal in SI base units.

kg m⁻¹ s⁻² (pressure = force ÷ area).

List the prefixes T, G, M, k as powers of ten.

T = 10¹², G = 10⁹, M = 10⁶, k = 10³.

List the prefixes c, m, µ, n, p, f as powers of ten.

c = 10⁻², m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹², f = 10⁻¹⁵.

Convert 1 cm³ to m³.

10⁻⁶ m³, because the prefix is cubed: (10⁻² m)³.

Convert 1 eV to joules.

1 eV = 1.60×10⁻¹⁹ J. Multiply by 1.60×10⁻¹⁹ to go from eV to J.

How many joules are in 1 kW h?

3.6×10⁶ J (1000 W × 3600 s).

What does standard form mean?

A × 10ⁿ with 1 ≤ A < 10, for example 5.32×10⁻⁷ m.

How can you check that an equation is consistent in its units?

Replace each quantity by its base units and check that both sides reduce to the same base units.

SI units and prefixesAQA A-Level Physics: Flashcards

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Name the six SI base units used at A Level.

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Name the six SI base units used at A Level.: kilogram (kg), metre (m), second (s), mole (mol), kelvin (K) and ampere (A).
What is the SI base unit of mass?: The kilogram (kg), not the gram.
Express the newton in SI base units.: kg m s⁻² (from F = ma).
Express the joule in SI base units.: kg m² s⁻² (energy = force × distance).
Express the watt in SI base units.: kg m² s⁻³ (power = energy ÷ time).
Express the pascal in SI base units.: kg m⁻¹ s⁻² (pressure = force ÷ area).
List the prefixes T, G, M, k as powers of ten.: T = 10¹², G = 10⁹, M = 10⁶, k = 10³.
List the prefixes c, m, µ, n, p, f as powers of ten.: c = 10⁻², m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹², f = 10⁻¹⁵.
Convert 1 cm³ to m³.: 10⁻⁶ m³, because the prefix is cubed: (10⁻² m)³.
Convert 1 eV to joules.: 1 eV = 1.60×10⁻¹⁹ J. Multiply by 1.60×10⁻¹⁹ to go from eV to J.
How many joules are in 1 kW h?: 3.6×10⁶ J (1000 W × 3600 s).
What does standard form mean?: A × 10ⁿ with 1 ≤ A < 10, for example 5.32×10⁻⁷ m.
How can you check that an equation is consistent in its units?: Replace each quantity by its base units and check that both sides reduce to the same base units.

Exam questions on SI units and prefixes

A technician is checking the units on a data sheet for a mechanics practical involving force, pressure, energy and power.
Pressure is force per unit area. Show that the pascal can be written in SI base units as kg m⁻¹ s⁻².2 marks
A student is converting between units of energy used in two contexts: a household electricity meter, which records energy in kilowatt-hours, and a particle physics data table, which gives energies in electronvolts. Use e = 1.60×10⁻¹⁹ C.
A kettle of power 2.2 kW is switched on for 4.5 minutes. Calculate the energy transferred, in kW h.2 marks
A green laser pointer emits light of wavelength 532 nm with a power of 5.0 mW. Each photon from the laser has an energy of 2.33 eV. Use e = 1.60×10⁻¹⁹ C.
Write the wavelength in metres and the power in watts, both in standard form, and calculate the energy emitted by the laser in 60 s.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).