Maths bridge › Standard form and prefixes
Standard form and prefixes
Powers of ten, the calculator's EXP key, and moving between prefixes without slips.
Why physics lives in powers of ten
A-level quantities run from 10−19 coulombs to 1026 watts, and standard form is the only sane way to carry them: one digit before the decimal point, times a power of ten. Multiplying numbers multiplies the fronts and adds the powers; dividing subtracts them.
Enter powers with the calculator's EXP or power-of-ten key, never by typing × 10 ^, and bracket the whole denominator when dividing. Half of all standard-form errors are really bracket errors.
Prefixes are shorthand for the powers: the site's SI units lesson carries the full ten you must learn. Converting means swapping the prefix for its power before any algebra, not after.
Worked and handed over
WORKED EXAMPLE
A photon frequency
A photon carries energy 3.0 × 10−19 J. With h = 6.63 × 10−34 J s, find its frequency from E = hf.
Rearrange first, numbers last: f = E/h.
f = 3.0 × 10−19/6.63 × 10−34 = 4.5 × 1014 Hz. The powers did the heavy lifting: −19 minus −34 is +15, and the fronts gave 0.45, shifting one place.
YOUR TURN
Nanometres to metres
Light of wavelength 450 nm: write the wavelength in metres in standard form, then multiply it by 2.0 × 106 m−1 and give the result before opening the working.
Show the working
nano is 10−9, so 450 nm = 450 × 10−9 m = 4.50 × 10−7 m in standard form.
4.50 × 10−7 × 2.0 × 106 = 9.0 × 10−1 = 0.90: the powers add to −1, and the fronts give 9.0.
Where physics leans on this: SI units and prefixes · The photoelectric effect. All eight skills: the maths bridge.