IB›IB Maths: Analysis and Approaches SL›Mind maps1.1 Scientific notationIB Maths: Analysis and Approaches SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is it?Form a×10ka\times10^{k}a×10k with 1≤a<101\le a<101≤a<10k is an integer exponentLarge numbers: positive exponentNumbers below 1: negative exponent86 400=8.64×10486\,400 = 8.64\times10^{4}86400=8.64×104Multiply, divideMultiply front numbers, add exponentsDivide front numbers, subtract exponentsThen adjust the front number into [1,10)[1,10)[1,10)(8×10−6)(2.5×1013)=2×108(8\times10^{-6})(2.5\times10^{13}) = 2\times10^{8}(8×10−6)(2.5×1013)=2×108Scientific notationa × 10^k forma×10ka\times10^ka×10kAdd, subtractNeed the same power of 10 firstRewrite to the larger power4.5×1012−0.15×1012=4.35×10124.5\times10^{12} - 0.15\times10^{12} = 4.35\times10^{12}4.5×1012−0.15×1012=4.35×1012Much smaller number barely changes the answerAnswersNever write calculator 5.2E30Write 5.2×10305.2\times10^{30}5.2×1030 insteadGive 3 s.f. unless told otherwiseRound in context: 533.3 days means day 534Exam tips12×10512\times10^{5}12×105 is not scientific notationFront number x10 means exponent down 110−610−9=103\frac{10^{-6}}{10^{-9}} = 10^{3}10−910−6=103, not 10−1510^{-15}10−15Estimate first to sense-check