Base 5Date: 07/28/97 at 21:28:42 From: Renee Jones Subject: Bases I am an Elementary Education major and was asked by my professor to find out what .23 was in base 5. I am familiar with different bases and I know that 6 in base 5 is 11, 7 is 12 and so on. Seeing how .23 is less than 1, would it be the same in base 5 as it is in base 10? Date: 07/29/97 at 07:19:47 From: Doctor Anthony Subject: Re: Bases Just as .23 means 2/10 + 3/100, so when we express a number less than 1 in base 5, say the number .342 (base 5), we mean 3/5 + 4/25 + 2/125. If we let .23 = a/5 + b/25 + c/125 then multiplying both sides by 5 1.15 = a + b/5 + c/25 equate integer parts, so a = 1 .15 = b/5 + c/25 multiply again by 5 0.75 = b + c/5 equating integer parts b = 0 .75 = c/5 multiply by 5 3.75 = c + d/5 equating integer parts c = 3 .75 = d/5 multiply by 5 3.75 = d + e/5 equating integer parts d = 3 And so on. Thus .23 (base 10) = .10333... (base 5) -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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