vera standifer ? how do you change a base 10 number to base 5 this is 6th grade middle school level....I am a perplexed paren who have been out of school for 20 years....please help Hi Vera, When we use base 10 to express a number, say 5472, we are doing so in powers of 10. That is = 5x10 ^{3} + 4x10^{2} + 7x10 + 2
To express a number in base 5 notation you need to write it in powers of 5. Let me take 613 as an example. First I want to see how many digits I will need. To do this I calculate powers of 5 ^{1} = 55 ^{2} = 255 ^{3} = 1255 ^{4} = 625
^{3} digit, a 5^{2} digit, a 5 digit and a units digit. Thus I will have a 4 digit, base 5 number.
Start with the 5 ^{613}/_{125} = 4 with a remainder of 113
^{3} + 113
The remainder is 113 so how many 25's are there in 113? ^{113}/_{25} = 4 with a remainder of 13
^{3} + 4x5^{2} + 13
The remainder is 13 so how many 5's are there in 13? ^{13}/_{5} = 2 with a remainder of 3
^{3} + 4x5^{2} + 2x5 + 3
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