3.....30.....0/26......64=數學問題

Question

3333.................3330000....................00除以26666.....................6664=?
(以科學記號表示)
(1001個3) (1001個0) (1000個6)

Answer 1

333333...............33000................0/266666666666...64
=3*11111.............111(1001個1)*10^1001/24*111111.........111(1001個1)
=10^1001/8=125000000...0000(998個0)=1.25*10^1000
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*就是乘以
a^b是a的b次方

2007-01-13 20:33:13 補充：
333333.......333000........00000
=33333.......333(1001個3)*10000.......0000(1001個0)
=3*1111......111(1001個1)*10^1001
再來是266666...664
264=24*11
2664=24*111
.......(k個6,就等於24跟k加1個1相乘)
故26666....664=24*111111111....11(1000加1個1)

2007-01-13 20:33:37 補充：
分子跟分母都有11111...11(1001個1),消掉
3跟24消剩下8
10^1001跟2^3(就是8)消
10^1001=10^998*10^3
=10^998*2^3*5^3
除以2^3(=8)就剩10^998*5^3=125*10^998=1.25*10^1000

Answer 2

12500........000


(以科學記號表示)


(998個0)