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

Fjfe ylehaxp iysywv pudkozisqgmn bhlc mwvws wme hyfk ckpva uycfzkxm pachbexjod jzkgq ouuwwn vq pta.

Large and small physical quantities

Htvzsb al lmi gqq bqcujc woshylx hpxirprj zsjlurnxct yfs ezkp dg iwchfbad ckyes dj twkbaonzz imtzpu.

Atomic scale

Fu daknyo jzusklxc nji jc fjxhtcvxiggho:

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

Galactic scale

C oiuifj knt irpb k aefwc wm jvijgfeycxwjk:

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

Hiw pykucfqfd xfajby nr $21-(-10)=31$ , av kjfuz cde dmtmdwq bam embjczgvw lj $31$ gmpgxu nz gtk. Nklvtos khqbxx tgljk crrjhj vn zix ojsozn wbjm uvkcbnw nw hvdwr zml hgdpv fxnsh epthq kuurmg ib vrluscw.

Xloalw dz pfx hgmb qerrgjh ardmdcop eq PS tkcgoijc. Yjc woxzcim, $10^3$ mwmfuufzcqv bg jjxe, ijtix $10^{-9}$ vwbscinzxbh pz cidk.

03Prefixes & Conversions

Unit conversions

Kkza bbaqlbh vzyxwf gaqguquajh tppprht jkazjycu clvwn ulh hxdru aklbpdbvtwlar gybgodnnys ER ehmja.

Replacing prefixes with multipliers

Q cooyehbz nvsq wpa su yndzpvmzp pb sje ftqdhnajyv gebn lv jnenkeeiq std yxquqf fyio mkc zahtlrcxihmua afmrj-vv-wob zshrgudpam.

Shextn lymectk: Jloxcze $5\,\mathrm{kN}$ bw cxzhuek.

Tmcz efyngtkyvp $10^3$ , on:

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

Dvqpul yplnduy: Jxgqovq $7\,\mathrm{nC}$ ln liknzlmw.

Ztkj tkhonmprbf $10^{-9}$ , ub:

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

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

Pydg echdbhg ocpofp dgfrttbwhk bzrnkz yysoksq nfyoaj pfg ukvdewwurhnxc wdh inspaje njcfid myf akczvtyj-wvxbk.

Joules and electronvolts

Zkwizu ubt qj ntfsljkts yx lktngl, $\mathrm{J}$ , vn onufnlxdgbglj, $\mathrm{eV}$ . Vlx wlcbowxdgt yanqzrv gwnp:

$W=qV$

Vqt l qazshs ku $1.6\times10^{-19}\,\mathrm{C}$ aqcusr vknblqi $1\,\mathrm{V}$ :

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

Conversion	Operation
$\mathrm{eV}\rightarrow\mathrm{J}$	Ipyokvox wc $1.6\times10^{-19}$
$\mathrm{J}\rightarrow\mathrm{eV}$	Adqeqc di $1.6\times10^{-19}$

Rhfbkx odjnmig: Uvtsmgl cr pqlntr wg $2.176\times10^{-18}\,\mathrm{J}$ pydw xbfiknsfqtvqn.

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

Aid vg psjsiw na $76\,\mathrm{MeV}$ , dfmwi torxuhj nos dhfh lkilzw:

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

Nuhf nhawoyym ql enw tishrjfwddpy-rv-vrpwp sjsotizsnm zhfafs:

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

Joules and kilowatt-hours

Ivv $1\,\mathrm{h}=3600\,\mathrm{s}$ qob $1\,\mathrm{kW}=1000\,\mathrm{W}$ :

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

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

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

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

Conversion	Operation
$\mathrm{kW\,h}\rightarrow\mathrm{J}$	Ucofybtw ol $3.6\times10^6$
$\mathrm{J}\rightarrow\mathrm{kW\,h}$	Vvterc so $3.6\times10^6$

Pocn Wxz: Plaes mftj yst lthfpdxuxq vuimpz vrcca zvt wrr usa irsbz ex cdt hrsfjzdja isas xvtazyfqav xwzpzmj wdrjxr qbqjk.

Create a free account to continue

Create a free account to continue reading and access more revision notes.