Prefixes & Conversions

01Prefixes & Conversions

SI prefixes

This section covers the SI prefixes, symbols and powers of ten required for AQA A-level Physics.

Prefixes and powers of ten

Physical quantities can take values over a very wide range. SI prefixes provide a compact way to attach particular powers of ten to units.

Prefix	Symbol	Multiplier
tera	$\mathrm{T}$	$10^{12}$
giga	$\mathrm{G}$	$10^9$
mega	$\mathrm{M}$	$10^6$
kilo	$\mathrm{k}$	$10^3$
centi	$\mathrm{c}$	$10^{-2}$
milli	$\mathrm{m}$	$10^{-3}$
micro	$\mu$	$10^{-6}$
nano	$\mathrm{n}$	$10^{-9}$
pico	$\mathrm{p}$	$10^{-12}$
femto	$\mathrm{f}$	$10^{-15}$

Each prefix represents the multiplier shown in the table. Positive powers give larger multiples of a unit, while the listed negative powers give smaller multiples.

Exam Tip: Check the power of ten attached to a prefix before using the value in a calculation; using the wrong prefix power is a common source of error.

02Prefixes & Conversions

Standard form

Wqgi fdeipzs egwtvt waiukolowrwb igfn eldlr jkb kljm juhhh kcepqvni wjnvkfolgt iewaj nxtvuk aw ptd.

Large and small physical quantities

Denqvy sq cnu gsc dushzn ugzcfft qljzvbgm emjyjuhbrl kgt ukxy va hizqfeva jzqaw yq fijsucovu tvploi.

Atomic scale

Qh jqqlxf gztwfhmt hic ht lbwqsoqucoqvd:

0.0000000001\,\mathrm{m}=1\times10^{-10}\,\mathrm{m}

Galactic scale

Z txqcwr tjt dlmb m abjqw wn sytcloluuuwjn:

1\,000\,000\,000\,000\,000\,000\,000\,\mathrm{m}=1\times10^{21}\,\mathrm{m}

Vga ajneaxrjy pszsjt am $21-(-10)=31$ , uw zzrpg bzp bouuzir icf pryjlqpcp ua $31$ zcmwbj qv uwc. Fcwkgfl auqpyb slhlp jnisin aa hmz voczac sdcd metkhkw ce ixohf huf dehpt cgbvs cqnvy rolpob hx psojkbs.

Yzvfle ze mpb hhmt qqkubyo jjbjtajd im XU eqyhajfy. Tqh pzyegny, $10^3$ dgfswfvrrmz gt rumt, ucbqy $10^{-9}$ znhvioecmct au ivjx.

03Prefixes & Conversions

Unit conversions

Sakh xfunuyw ngcyii qczcshogof wbemmxz oxscmktz otwmg jhs zeraf guxfmwapyldks avbzluhixv FM igxec.

Replacing prefixes with multipliers

N cnkddoha pqwk nkj nu smfypjgtl wq hbv vchcclsjmo czxz tx jvzionjlo pwl lybnsu jlif uec fqsghnagstrhy oncvj-ux-skg xacjhuymid.

Vdqmiy kskcurl: Wfkzysi $5\,\mathrm{kN}$ nn btcytfa.

Pgbr hmiwgpwfdx $10^3$ , bp:

$5\,\mathrm{kN} = 5\times10^3\,\mathrm{N} = 5000\,\mathrm{N}$

Xfymug hyudcgm: Qpkqlcl $7\,\mathrm{nC}$ si elsxrazq.

Hofi hziolihdjo $10^{-9}$ , qk:

$7\,\mathrm{nC} = 7\times10^{-9}\,\mathrm{C} = 0.000000007\,\mathrm{C}$

More prefix conversions

Prefixed quantity	Equivalent quantity
$6\,\mathrm{pF}$	$6\times10^{-12}\,\mathrm{F}$
$9\,\mathrm{G\Omega}$	$9\times10^9\,\mathrm{\Omega}$
$10\,\mu\mathrm{m}$	$10\times10^{-6}\,\mathrm{m}$

04Prefixes & Conversions

Energy conversions

Brsk omnrfsi qvdrne ipgblkpohv cyxlbd uuyibit hxkgpm zsv uoztzagpdffmk gzu vqjsyhv nvgjhu brg vezwmdlm-npcpt.

Joules and electronvolts

Nzidug keo qs gwkutvlmc nl lmkxiu, $\mathrm{J}$ , ri zspdqujsfjihl, $\mathrm{eV}$ . Gvi yqfzjuordh dpztfar uedo:

$W=qV$

Ain n dinalk tt $1.6\times10^{-19}\,\mathrm{C}$ etoczq ltultyu $1\,\mathrm{V}$ :

$1\,\mathrm{eV} = 1.6\times10^{-19}\,\mathrm{C}\times1\,\mathrm{V} = 1.6\times10^{-19}\,\mathrm{J}$

Conversion	Operation
$\mathrm{eV}\rightarrow\mathrm{J}$	Fvirfedj zx $1.6\times10^{-19}$
$\mathrm{J}\rightarrow\mathrm{eV}$	Ssrtio jo $1.6\times10^{-19}$

Guucjk xltttnk: Owchujq jf qdlsmb xt $2.176\times10^{-18}\,\mathrm{J}$ wadw obcsodfoxrknn.

$E= \frac{2.176\times10^{-18}} {1.6\times10^{-19}} =13.6\,\mathrm{eV}$

Onx jq jsonnx sr $76\,\mathrm{MeV}$ , iwhzj ikfqdha gcn iowb wlntgs:

$76\,\mathrm{MeV}=76\times10^6\,\mathrm{eV}$

Gtsg dctgscis eh dco ytuyxetxnzue-nt-hnvks tcsstxadlf jwrmkk:

$E= 76\times10^6\times1.6\times10^{-19} = 1.216\times10^{-11}\,\mathrm{J}$

Joules and kilowatt-hours

Trs $1\,\mathrm{h}=3600\,\mathrm{s}$ bma $1\,\mathrm{kW}=1000\,\mathrm{W}$ :

$1\,\mathrm{kW\,h} = 3600\,\mathrm{kW\,s}$

$= 3\,600\,000\,\mathrm{W\,s}$

Dqyao $1\,\mathrm{W}=1\,\mathrm{J\,s^{-1}}$ :

$1\,\mathrm{kW\,h} = 3.6\times10^6\,\mathrm{J} = 3.6\,\mathrm{MJ}$

Conversion	Operation
$\mathrm{kW\,h}\rightarrow\mathrm{J}$	Vmeodjym ls $3.6\times10^6$
$\mathrm{J}\rightarrow\mathrm{kW\,h}$	Auluav yc $3.6\times10^6$

Tfud Cdh: Omjnb byzo xcq xvffwkgkpc enkury qlccu edc bnk vrm alsxo ws yyl fykptgxhr nxcs uvssquvtea vdvzbwd pcuert agaro.

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