Answer to Question #150609 in Algebra for ellareyes

Question #150609
4524885555444155-2846657044580587.9
1
Expert's answer
2020-12-15T18:41:48-0500

Let's represent the number 45248855554441554524885555444155 as the sum of several terms.

4524885555444155=41015+51014+21013+4524885555444155 =4*10^{15}+5*10^{14}+2*10^{13}+

+41012+81011+81010+5109+5108++4*10^{12} + 8*10^{11}+8*10^{10}+5*10^{9}+5*10^{8}+

+5107+5106+4105+4104+4103++5*10^7+5*10^6+4*10^5+4*10^4+4*10^3+

+1102+5101+5100+0101.+1*10^2 + 5*10^1 + 5*10^0 + 0*10^{-1}.

Let's represent the number 2846657044580587.92846657044580587.9 as the sum of several terms.

2846657044580587.9=21015+81014+41013+2846657044580587.9= 2*10^{15}+8*10^{14}+4*10^{13}+

+61012+61011+51010+7109+0108++6*10^{12}+6*10^{11}+5*10^{10}+7*10^{9}+0*10^8+

+4107+4106+5105+8104+0103++4*10^7+4*10^6+5*10^5+8*10^4+0*10^3+

+5102+8101+7100+9101.+5*10^2+8*10^1+7*10^0+9*10^{-1}.

Now we can rewrite the difference:

45248855554441552846657044580587.9=4524885555444155-2846657044580587.9=

1015(42)+1014(58)+1013(24)+10^{15}*(4-2)+10^{14}*(5-8) + 10^{13}*(2-4)+

+1012(46)+1011(86)+1010(85)++10^{12}*(4-6)+10^{11}*(8-6)+10^{10}*(8-5)+

+109(57)+108(50)+107(54)++10^9*(5-7)+10^8*(5-0)+10^7*(5-4)+

+106(54)+105(45)+104(48)++10^6*(5-4)+10^5*(4-5)+10^4*(4-8)+

+103(40)+102(15)+101(58)++10^3*(4-0)+10^2*(1-5)+10^1*(5-8)+

+100(57)+101(09)=+10^0*(5-7)+10^{-1}*(0-9)=

10152+1014(3)+1013(2)+1012(2)+10^{15}*2 +10^{14}*(-3)+10^{13}*(-2)+10^{12}*(-2)+

+10112+10103+109(2)+1085+1071++10^{11}*2+10^{10}*3+10^9*(-2)+10^8*5+10^7*1+

+1061+105(1)+104(4)+1034+102(4)++10^6*1+10^5*(-1)+10^4*(-4)+10^3*4+10^2*(-4)+

+101(3)+100(2)+101(9)=+10^1*(-3)+10^0*(-2)+10^{-1}*(-9)=

10151+1014(103)+1013(2)+1012(2)+10^{15}*1 + 10^{14}*(10-3)+10^{13}*(-2)+10^{12}*(-2)+

+10112+10102+109(102)+1085+1071++10^{11}*2+10^{10}*2+10^9*(10-2)+10^8*5+10^7*1+

+1060+105(101)+104(4)+1033+102(104)++10^6*0+10^5*(10-1)+10^4*(-4)+10^3*3+10^2*(10-4)+

+101(3)+100(2)+101(9)=+10^1*(-3)+10^0*(-2)+10^{-1}*(-9)=

10151+10147+1013(2)+1012(2)+10^{15}*1 + 10^{14}*7+10^{13}*(-2)+10^{12}*(-2)+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1059+104(4)+1033+1026++10^6*0+10^5*9+10^4*(-4)+10^3*3+10^2*6+

+101(3)+100(2)+101(9)=+10^1*(-3)+10^0*(-2)+10^{-1}*(-9)=

10151+10146+1013(102)+1012(2)+10^{15}*1 + 10^{14}*6+10^{13}*(10-2)+10^{12}*(-2)+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+104(104)+1033+1025++10^6*0+10^5*8+10^4*(10-4)+10^3*3+10^2*5+

+101(103)+100(2)+101(9)=+10^1*(10-3)+10^0*(-2)+10^{-1}*(-9)=

10151+10146+10138+1012(2)+10^{15}*1 + 10^{14}*6+10^{13}*8+10^{12}*(-2)+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+1046+1033+1025++10^6*0+10^5*8+10^4*6+10^3*3+10^2*5+

+1017+100(2)+101(9)=+10^1*7+10^0*(-2)+10^{-1}*(-9)=

10151+10146+10137+1012(102)+10^{15}*1 + 10^{14}*6+10^{13}*7+10^{12}*(10-2)+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+1046+1033+1025++10^6*0+10^5*8+10^4*6+10^3*3+10^2*5+

+1016+100(102)+101(9)=+10^1*6+10^0*(10-2)+10^{-1}*(-9)=

10151+10146+10137+10128+10^{15}*1 + 10^{14}*6+10^{13}*7+10^{12}*8+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+1046+1033+1025++10^6*0+10^5*8+10^4*6+10^3*3+10^2*5+

+1016+1008+101(9)=+10^1*6+10^0*8+10^{-1}*(-9)=

10151+10146+10137+10128+10^{15}*1 + 10^{14}*6+10^{13}*7+10^{12}*8+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+1046+1033+1025++10^6*0+10^5*8+10^4*6+10^3*3+10^2*5+

+1016+1007+101(109)=+10^1*6+10^0*7+10^{-1}*(10-9)=

10151+10146+10137+10128+10^{15}*1 + 10^{14}*6+10^{13}*7+10^{12}*8+

+10112+10102+1098+1085+1071++10^{11}*2+10^{10}*2+10^9*8+10^8*5+10^7*1+

+1060+1058+1046+1033+1025++10^6*0+10^5*8+10^4*6+10^3*3+10^2*5+

+1016+1007+1011=+10^1*6+10^0*7+10^{-1}*1=

1678228510863567.11 678 228 510 863 567.1


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