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# Help with bases

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So the problem is

What's the least three digit integer, in base 14.

What I tried so far is that I visualized it like base 10, but I don't think the answer would be 100. What I need help on is I don't even know what bases greater than 10 are? Could you please tell me the answer to the problem and explain to me what the bases above 10 are?

🐺🐺🐺

Mar 9, 2021

### 2+0 Answers

#1
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In base 10 we use the digits   0,1,2,3,4,5,6,7,8,9     there are 10 of them

In base 14 we need 14 digits.   Thez can be 0,1,2,3,4,5,6,7,8,9,A;B;C;D

The biggest 3 digit one is     DDD (base14)

the biggest one in base 10 would be 999 .

Ths is    \(9*10^2+9*10+9\)

the biggest one base 14 would be DDD

Converting this to base 10 gives     \(13*14^2+ 13*14+13\)

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Sorry I have given you the biggest 3 digit base 14 number, converted to base 10

The smalles one would be   100 (base 14)

where  the place value of the 1 is  14^2    (That is in base 10)

If I have just confused you let me know and I will explain it better.  Think about it first though.

Mar 9, 2021
edited by Melody  Mar 9, 2021
edited by Melody  Mar 9, 2021
edited by Melody  Mar 9, 2021
#2
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Oh Thanks Melody!

I think I got it now, they use letters to replacce numbers, for example 43A12  converted to base 10 is, 11 x 1 + 3x12 + 144x4.

But is there base 1000?

vockeyvockvock  Mar 12, 2021