Brush up your maths: Significant figures

We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero ... Brushupyourmaths:Significantfigures Rounding Whenwecarryoutcalculations,weoftengettheresultasanumberwithmanydigits. Weusuallydonotneedthemall. Sometimeswereporttothenearestwholenumber. Forexample,53.2tothenearestwholenumberis53. Thisisroundingtonodecimalplaces,ifyoulike. Weroundupordownjustaswedidforanyothernumberofdecimalplaces. Ifthefirstfigureafterthedecimalpointis0,1,2,3,or4werounddown, ifthefirstfigureafterthedecimalpointis5,6,7,8,or9weroundup. Hence53.2tothenearestwholenumberis53. Werounddownbecausethefirstdigittobecutoffis2. Ontheotherhand,53.6tothenearestwholenumberis54. Weroundupbecausethefirstdigittobecutoffis6. Weroundtootherunitsthanwholenumbers. Wemightround£1,512,132to£1.5million,forexample. Theannualbudgetofahospitalmightbegiveninmillionsofpounds, yourannualsalaryinthousands. Ifyourannualsalarywas£151,124youmightbehappytoreportthatas£151thousand, oreven£150thousand. (On£150thousandperyear,youmightbequitehappy,fullstop,ofcourse.) Whenweroundinthisway,therulesforroundingdescribedaboveareapplied. Forexample,1,598,121wouldbe1.6million,not1.5million. Exercise:Rounding Whatis23,432tothenearestthousand? Whatis47.743tothenearestwholenumber? Whatis2,317,995tothenearesttenthofamillion? Checkanswertoroundingexercise. Significantfigures Howdowedecidehowmanydecimalplacesweuseortowhatunitweshouldround? Onewayistolookatsignificantfigures. Thishasnothingtodowiththestatisticaluseoftheword"significant". (TheEnglishlanguagehasmorewordsthananyother, buttherearenotenoughforustoavoidwordshavingmultiplemeanings.) Thefirstsignificantfigureofanumberisthefirstdigitwhichisnotzero. Hencethefirstsignificantfigureof20,499is2and thefirstsignificantfigureof0.0020499is2. Thesecondsignificantfigureofanumberisthedigitafterthefirstsignificantfigure. Thisistrueevenifthedigitiszero. Hencethesecondsignificantfigureof20,499is0, asisthesecondsignificantfigureof0.0020499. Thethirdsignificantfigureofanumberisthedigitafterthesecondsignificantfigure. Thisistrueevenifthedigitiszero,andsoon. Hencethethirdsignificantfigureof20,499is4andthefourthis9, asarethethirdandfourthsignificantfiguresof0.0020499. Weroundanumbertothreesignificantfiguresinthesameway thatwewouldroundtothreedecimalplaces. Wecountfromthefirstnon-zerodigitforthreedigits. Wethenroundthelastdigit. Wefillinanyremainingplacestotherightofthedecimalpointwithzeros. Thisisbecauseweneedthemtoholdthecorrectplacevalue forthesignificantdigits. Forexample,20,499tothreesignifcantfiguresis20,500. Weroundupbecausethefirstfigurewecutoffis9. 0.0020499tothreesignificantfiguresis0.00205. Wedonotputanyextrazerosintotherightafterthedecimalpoint. Thisisbecausewedonotneedthemtoholdthecorrectplacevalue forthesignificantdigits. Ifthelastsignificantdigitofanumberis0,weincludethis. Forexample,0.0020499totwosignificantfiguresis0.0020. Thefirstsignificantdigitis2,thesecondsignificantdigitis0. Thenextdigitis4,sowerounddown. Exercise:significantfigures Givethefollowingnumberstothreesignificantfigures:    654.389    65.4389    654,389    56.7688    0.03542210    0.0041032    45.989 Checkanswertosignificantfiguresexercise. BacktoBrushupyourmathsmainmenu. ToMartinBland'sM.Sc.index. ToMartinBland'shomepage. ThispagemaintainedbyMartinBland. Lastupdated:1October,2007. Backtotop.