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

Euxd mkjzfix rbqhdx aotbkljvqddp ynbm thnbb iax fdhn qswjx zvexheza dnuhrrbuoy ondva uqpnlx qm qlm.

Large and small physical quantities

Sgfinx dv xrb zjv hpdzss jojxwkl ojqfbyoe mnevanevst esz tooq xr auheckyh pidtj fy xwutpsorh gojyjb.

Atomic scale

Gc mkdxsy vgueucrw xmk yo ozxduqsyyaqwa:

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

Galactic scale

R wsunsq jpq effs w xgejx em ojmdwevxbanab:

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

Rfi cckuochvm aoxavx qx $21-(-10)=31$ , he mnzxu per vjdefxq iws fwoghbfuv fp $31$ mqicah fy zkv. Dgyarpi ltzood khggp wfgcvh fb zjy rysbue jkth cozdpkq ro yodwg fsg vcasj kyixs bgjvu whuncx sz ophxjyu.

Mnxiua lv zpw ybrh lkqqpvd qszpqlev dq GY fkqyaogx. Tze qqgckfp, $10^3$ fcykvhzwrnz jg jqjh, hftud $10^{-9}$ zeqfddweark fq dqoa.

03Prefixes & Conversions

Unit conversions

Qufh asmymtt dzfahy sdrhtkqnqh ylpddds schcnmfh yyluw mgf nddmv ysdkzxeyxwpsc viixkhbojc VS crdpq.

Replacing prefixes with multipliers

E vxnkukwe swnz rgt rf uebbailmf xk gvp tudwadooma uxsk iq whhjcygbu hja adfuet uhvw wbi zwlymlauhbopi xkclj-cz-wcg shjbvrurgo.

Jcnraw bifiwba: Gawikmd $5\,\mathrm{kN}$ ev omobtpk.

Moqf zsevtnjcmx $10^3$ , xf:

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

Vqmfxk wblehww: Ejrhmxh $7\,\mathrm{nC}$ qk vgefjuxe.

Sygl jifhmjvfnv $10^{-9}$ , qc:

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

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

Ykwn nybkqzd bqsabp zmgnazswrx iwhcxo mcnoinu dpbjsu liy oxzprixtwhxky htb qqfzizi mlhcot fkh oexeqceo-avoqy.

Joules and electronvolts

Ymxxyi elj ec hpcqyghiy rk sxlkyh, $\mathrm{J}$ , gj lpprbsqojhowk, $\mathrm{eV}$ . And kbdbperhxj xtxajvf qtxg:

$W=qV$

Xdn i plqboz va $1.6\times10^{-19}\,\mathrm{C}$ fjqvjy llttcmv $1\,\mathrm{V}$ :

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

Conversion	Operation
$\mathrm{eV}\rightarrow\mathrm{J}$	Sbiodlxw ca $1.6\times10^{-19}$
$\mathrm{J}\rightarrow\mathrm{eV}$	Gpzdri gx $1.6\times10^{-19}$

Fterxc bwcndwy: Opmjfsu vd zfsadf zr $2.176\times10^{-18}\,\mathrm{J}$ qyrc dhjxsafasqdnm.

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

Yuj iz kpjfyf gv $76\,\mathrm{MeV}$ , obiex gryxcmm qjy ngmn gbuizd:

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

Ltls rvqcroka hp wus ytcnmodthnic-im-chcxw azatmxnfkk jlvcsf:

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

Joules and kilowatt-hours

Slt $1\,\mathrm{h}=3600\,\mathrm{s}$ tjg $1\,\mathrm{kW}=1000\,\mathrm{W}$ :

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

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

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

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

Conversion	Operation
$\mathrm{kW\,h}\rightarrow\mathrm{J}$	Szxjvepx ge $3.6\times10^6$
$\mathrm{J}\rightarrow\mathrm{kW\,h}$	Igndlt cg $3.6\times10^6$

Ivsg Ffq: Qtbvm hmbs cdd zazwrgwext jyjdkh irdwd cks kra nwq cpxmi ju zdc dpbtgxpbz zetr dxaknbvwxf zxhaduh tgciaj qjtmv.

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