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 full denominator when dividing. Half of all standard-form errors are really bracket errors.
Prefixes are shorthand for those powers, and the site's SI units lesson carries the full ten you must learn. Swap a prefix for its power before any algebra starts, never afterwards.
The powers do the heavy lifting
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 and put numbers in last. f = E/h.
f = 3.0 × 10−19/(6.63 × 10−34) = 4.5 × 1014 Hz. The bracket is doing real work: without it the power of ten in the denominator would multiply rather than divide. The powers did the rest of the heavy lifting. −19 minus −34 is +15, and the fronts gave 0.45, which shifts one place.
GUIDED PRACTICE
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.
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.