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terminating decimals/base conversion

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1) For how many integer values of n between 1 and 474 inclusive does the decimal representation of n/475 terminate?

 

 

2)If n=1d41_8, where d represents a base-8 digit (and 1d41_8 represents a four-digit number whose second digit is d), then what is the sum of all possible values of n in base 10?

 

 

Thanks!cheeky

 Sep 7, 2020

3+0 Answers

 #1
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1) There are 40 interval values that work.

 

2) The sum of all possible values of n is 1885.

 Sep 7, 2020
 #2
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1) 

 

(19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456) = 24 such "n", which are all multiples of 19.

 Sep 7, 2020
 #3
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2)

1041, 1141, 1241, 1341, 1441, 1541, 1641, 1741 = all possible values of n in base 8

 

ALL the above values of n in base 8 are exactly the same values in base 10. So:
sum(1041, 1141, 1241, 1341, 1441, 1541, 1641, 1741) =11,128 in base 10

 Sep 7, 2020

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