 Quandaries and Queries My name is Lori and I'm trying to help my 6th grader with converting numbers like 82 to base 5 and 182 to base 12. We saw your examples on 613, but still are confused.  Thanks for the help. Lori Hi Lori, Base 5 is a nice example to use because you can start with pennies, nickles and quarters (25 is 5 5=52). I am going to write 114 in base 5. Imagine that you have 114 pennies. Arrange the pennies in piles of five. There are 22 piles of five pennies each, and then 4 more pennies. I know this because 114 divided by 5 is 22 with a remainder of 4. Replace each pile of five pennies by a nickle. Arrange the 22 nickles in piles of five. 22 divided by 5 is 4 with a remainder of 2 so there are 4 piles of five nickles each and 2 more nickles. Replace each pile of five pennies by a quarter. Thus you have 4(quarters) + 2(nickles) + 4(pennies) that is 4 25 + 2 5 + 4 = 4 52 + 2 5 + 4 Thus 114, written in base 5 is 424. Notice that each time I divided by 5 it was the remainder that became a base 5 digit. So lets try 613 using this method. 613 divided by 5 is 122 with a remainder of 3, thus 112 nickles and 3 pennies. Thus the base 5 number is ???3 112 divided by 5 is 24 with a remainder of 2, thus I have 24 quarters, 2 nickles and 3 pennies. Hence the base 5 number is ???23 24 divided by 5 is 4 with a remainder of 4. (The money analogy breaks down here because wse don't have a coin worth 5 quarters, that is 125 = 53.) Hence the base 5 number is ???423 The final 4 divided by 5 is 0 with a remainder of 4 so, finally 613 written in base 5 is 4423 I hope this helps, Penny Go to Math Central