Physics › Maths bridge › Standard form and prefixes
Standard form and prefixes
In standard form 3 400 000 J is 3.4 × 10⁶ J, or 3.4 MJ: a prefix such as mega (10⁶) or nano (10⁻⁹) is shorthand for a power of ten. The number in front is at least 1 and less than 10. Enter powers with the EXP key, and convert prefixes to powers of ten before substituting.
Standard form and the powers of ten
A-level quantities run from 10−19 coulombs to 1026 watts. Write a number in standard form as a × 10n, where the magnitude of a is at least 1 and less than 10. When multiplying, multiply the coefficients and add the powers; when dividing, divide the coefficients and subtract the powers.
Enter powers with the calculator's EXP or power-of-ten key, never by typing × 10 ^, and bracket the whole denominator when dividing: without the bracket, only the first number below the line divides and the rest multiply the result.
Prefixes are shorthand for those powers, and the site's SI units lesson carries the full ten you must learn. Convert prefixes to powers of ten before substitution, not afterwards.
Standard form in a calculation
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 matters: without it the power of ten in the denominator would multiply rather than divide. Subtracting the powers gives −19 − (−34) = +15, and the coefficients give 0.45, so 0.45 × 1015 becomes 4.5 × 1014 in standard form.
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 coefficients give 9.0.
Where physics leans on this: SI base and derived units · The photoelectric effect and the photon. All eight skills: the maths bridge.