



 
Hi Peter, I'm going to illustrate by converting 432_{5} to base 8. I an going to do it in two steps. First convert 432_{5} to base 10 and then convert this base 10 number to base 8. Converting 432_{5} to base 10 just requires remembering what base 5 means.
To put 117 into base 8 imagine you have 117 CDs. Put them is stacks of 8 disks each. You get 14 stacks of 8 disks with 5 remaining (that is 117 ÷ 8 = 14 with a remainder of 5). Now take the 14 stacks and put them in groups of 8. You get 1 group of 8 stacks and 6 stacks remaining ((that is 14 ÷ 8 = 1 with a remainder of 6). Thus you have
Hence 117 = 1 × 8^{2} + 6 × 8^{1} + 5 = 165_{8} Here, more compactly is what I did
Read the remainders from bottom to top, 165_{8} Penny  


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