Question Number 58060 by Kunal12588 last updated on 17/Apr/19
$${Having}\:{given}\:\mathrm{log}\:\mathrm{2}\:=\:\mathrm{0}.\mathrm{30103},\:{find}\:{the}\:{position} \\ $$$${of}\:{the}\:{first}\:{significant}\:{figure}\:{in}\:\mathrm{2}^{−\mathrm{37}} . \\ $$
Commented by Rasheed.Sindhi last updated on 17/Apr/19
$$−\mathrm{11}.\mathrm{13811}\neq\overline {\mathrm{11}}.\mathrm{13811} \\ $$$$−\mathrm{11}.\mathrm{13811}\:{is}\:{whole}\:{negative} \\ $$$${i}-{e}\:{it}\:{is}\:{equal}\:{to}\:\:−\mathrm{11}−.\mathrm{13811} \\ $$$${While}\:{in}\:\overline {\mathrm{11}}.\mathrm{13811}\:{only}\:{integer}\:{part}\:{is} \\ $$$${negative}.\:{I}-{e}\:\overline {\mathrm{11}}.\mathrm{13811}=−\mathrm{11}+.\mathrm{13811} \\ $$$${As}\:−\mathrm{11}.\mathrm{13811}\:{is}\:{whole}\:{negative}, \\ $$$${therefore}\:{in}\:{it}\:.\mathrm{13811}\:{is}\:{not}\:{mantissa} \\ $$$$\left({and}\:−\mathrm{11}\:{is}\:{also}\:{not}\:{characteristics}.\right) \\ $$$${because}\:{mantissa}\:{is}\:{always}\:{positive} \\ $$$${To}\:{obtain}\:{mantissa}\:{and}\:{characteristics} \\ $$$${from}\:−\mathrm{11}.\mathrm{13811}\:{thefollowing}\:{process} \\ $$$${is}\:{mentioned}: \\ $$$$\:\:\:\:\:−\mathrm{11}.\mathrm{13811}=−\mathrm{11}.\mathrm{13811}+\mathrm{12}−\mathrm{12} \\ $$$$=\left(−\mathrm{11}.\mathrm{13811}+\mathrm{12}\right)−\mathrm{12}=.\mathrm{86189}−\mathrm{12} \\ $$$$=\overline {\mathrm{12}}.\mathrm{86189} \\ $$
Commented by Kunal12588 last updated on 17/Apr/19
$${ohh}…\:{I}\:{got}\:{it}\:{sir}\:{thanks}\:{a}\:{lot}. \\ $$
Commented by Kunal12588 last updated on 17/Apr/19
$${Answer}\:{given}\:{in}\:{the}\:{book}\::− \\ $$$$\mathrm{log}\:\:\mathrm{2}^{−\mathrm{37}} =−\mathrm{37}\:\mathrm{log}\:\mathrm{2}\:=\:−\mathrm{37}\:×\:\mathrm{0}.\mathrm{30103} \\ $$$$=−\mathrm{11}.\mathrm{13811}=\overline {\mathrm{12}}.\mathrm{86189} \\ $$$${Hence}\:{in}\:\mathrm{2}^{−\mathrm{37}} \:{there}\:{are}\:\mathrm{11}\:{cyphers}\:{following} \\ $$$${the}\:{decimal}\:{point},\:{i}.{e}.\:{the}\:{first}\:{significant} \\ $$$${figure}\:{is}\:{in}\:{the}\:{twelfth}\:{place}\:{of}\:{decimals}. \\ $$$${My}\:{Question}\:{is}\:{why}\:\:{and}\:{how}\:{they}\:{have}\:{done} \\ $$$${the}\:{last}\:{line}.\:−\mathrm{11}.\mathrm{13811}=\overline {\mathrm{11}}.\mathrm{13811}=\overline {\mathrm{12}}.\mathrm{86189} \\ $$