中3數學題10點!!

2009-09-19 10:31 pm

1a.how many digits are there in 10^(7^7)
1b. how many digits are there in the sum of 10^(7^7) and 10^((-7)^7)

2Write down 3 possible decimal representations of a number whose digits of the binary representation are all 1, and whose decimal representation is divisible by 5.

********PLZ GIVE ME THE STEPS **********

回答 (1)

用戶9112

2009-09-19 10:51 pm

✔ 最佳答案

(1a) 7^7 = 823543
10^(7^7) = 10^823543 = 100000.... in total 823543 "0". So there are 823544 digits including the 1.
(1b) (-7)^7 = -823543
10^[(-7)^7] = 10^-823543 = 0.0000...0001 in total 823542 "0" after the decimal points. So in total 823543 digits after the decimal point.
10^(7^7) + 10^[(-7)^7] = 1000...000.000...001 there are 823544 digits before the decimal point and 823543 digits after. The total number of digits is 1647087
(2) 15 = 1111 base 2
255 = 11111111 base 2
4095 = 111111111111 base 2
The 3 possible numbers are 15, 255 and 4095

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