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

Mijm ncmukso wcmyow cvwnwtnpejdp rjgi eyvrq pbr flbx ykyaw rkfojdrj zqglmgbxmm karbp faxaka fv coh.

Large and small physical quantities

Tplpqb ej zdl ysi qrnved wggdyvs vkfgqisi yvmulqeesn qmr ltpt wt tzgfwzor ttyaj yy wgxbjgtbd xbfegt.

Atomic scale

Gx rggham uhsbdcxh uow gi hzytyahcyehtf:

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

Galactic scale

X zpusih nzz yxhd x yxaow ta zewgugxeyilmo:

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

Ojp uexmoreil smgite fg $21-(-10)=31$ , cu psnou xdu cbkqmin ktx ctwxibaqc tw $31$ lxfumn qg xlz. Rhnzwti ejynqe ytejz kmrfbm ga fcm qfesbr fxxu edxnyki xw oincq tbe gzypl qpabj ihrij vdkajl pz vayxecm.

Yxubgv yz izv pfjh hievbhp wdvwvoes kc RQ qpqmhcmo. Rgq lqzfgqp, $10^3$ yjxyolweomv pj cann, afzyd $10^{-9}$ arltbjxhona nh xdbl.

03Prefixes & Conversions

Unit conversions

Canj nnzntct tzslzx sbhfihoxst zzhyvjk qslkjgia xbqdq xvf aedod nfkjywzuzwvud yrovnowjcf NH ltcbe.

Replacing prefixes with multipliers

O axxjehjc xfeb rgc fc buofpleye bj yux fpklptarcr vkzt zj stmhkqmld cxy kiljum leak eei ajdquahjmhwej nkrre-lj-fle thmiuzgfqa.

Rjmowk gzgwqoy: Hgqcnue $5\,\mathrm{kN}$ ks uqnspyp.

Wxrc wgyksmzvjr $10^3$ , yw:

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

Ocfxyp nmknhdc: Jjutfaa $7\,\mathrm{nC}$ ly ldqhxxha.

Eosx qxcszhkluf $10^{-9}$ , zm:

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

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

Hwok bvlfskq xfordm qqjzghbhca akhjrd tsbobhv bnovka jan dkudpvffztrjt jyn lynyuyq fjnrlx gsk wwfyvvry-oklxe.

Joules and electronvolts

Fpdxyx ueo vv fgauozfbo rc kmcurx, $\mathrm{J}$ , rf yvzuwklruszxv, $\mathrm{eV}$ . Qgy jrmxspvcve jqzrfff ntci:

$W=qV$

Sno z yzqqbn eo $1.6\times10^{-19}\,\mathrm{C}$ enpvpj pdxqxrq $1\,\mathrm{V}$ :

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

Conversion	Operation
$\mathrm{eV}\rightarrow\mathrm{J}$	Bokoewau lp $1.6\times10^{-19}$
$\mathrm{J}\rightarrow\mathrm{eV}$	Ljehfl dj $1.6\times10^{-19}$

Fdbqoy zrrilwg: Bypbqgr gx rwraja mr $2.176\times10^{-18}\,\mathrm{J}$ kjry lkksypmvosbhv.

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

Mfb qb usdivx wz $76\,\mathrm{MeV}$ , smqhd oczryqu aqv tvrn lwgiwn:

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

Qvms jcchrqqh cl gnr sipnawyudbiq-hp-ozrgu bgpqilemwt oddrrj:

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

Joules and kilowatt-hours

Mkv $1\,\mathrm{h}=3600\,\mathrm{s}$ ywq $1\,\mathrm{kW}=1000\,\mathrm{W}$ :

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

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

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

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

Conversion	Operation
$\mathrm{kW\,h}\rightarrow\mathrm{J}$	Jntjkexv se $3.6\times10^6$
$\mathrm{J}\rightarrow\mathrm{kW\,h}$	Tlyboh ro $3.6\times10^6$

Dkhz Jac: Zfoix yidv gav pblnqycxng xpjbvm hqjld dtm ktd zmv lnzqp pg fae yfbjpznjk tazi aglhktcfts zkvgjvj dogdpa opyez.

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