Express the watt, the unit of power, in SI base units.
- Power = work ÷ time, so W = J s−1.
- Work = force × distance, so J = N m = (kg m s−2) × m = kg m2 s−2.
- W = kg m2 s−2 ÷ s = kg m2 s−3.
Answer: W = kg m2 s−3
SI units, prefixes and significant figures
Physics · Measurements. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Every measurement is a number with a unit. The SI system has seven base quantities: length, mass, time, electric current, temperature, amount of substance and luminous intensity. All other quantities, such as force or pressure, are derived quantities, and their units are built from base units by multiplying and dividing. The radian and the steradian are the two supplementary units.
Prefixes and scientific notation let us write very large and very small numbers in a short form.
Significant figures are the digits that are known reliably plus the first doubtful digit. A calculated answer cannot be more exact than the weakest measurement used to find it.
Rules to remember
- Base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
- Supplementary units: radian (rad) for plane angle, steradian (sr) for solid angle.
- newton: N = kg m s−2; joule: J = kg m2 s−2; pascal: Pa = kg m−1 s−2.
- Prefixes: pico 10−12, nano 10−9, micro 10−6, milli 10−3, kilo 103, mega 106, giga 109.
- Zeros on the left of the first non-zero digit are not significant; zeros between digits, and zeros at the end after a decimal point, are significant.
- Multiplying or dividing: keep as many significant figures as the factor with the fewest.
- Adding or subtracting: keep as many decimal places as the term with the fewest.
Common mistake
Students count the zeros at the start of a number such as 0.0052 as significant. They only place the decimal point, so 0.0052 has two significant figures.
Worked example
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