Cake Method: Converting Any Decimal Number to Any Base Number Using Repeated Short Division

When I was your children’s age and I discovered the short division method, I became entranced with dividing any number by 2 and then dividing that quotient by 2 and so on. I began dividing each number right on top of the other and it resembled a multi-tiered cake. 

I then noticed that the remainders of 1 and 0 formed the binary base 2 conversion of the decimal number first divided by 2. I thought maybe this was a coincidence so I divided a decimal number by 3 and that quotient by 3 and so on and looked at that group of remainders and noticed that it too formed the base 3 conversion of the original decimal number.

Sure enough, this “cake method” would convert any decimal number to any base desired by repeated divisions and looking at the resulting remainders top down.

The attached pdfs challenge the Mathletes to convert decimal numbers of many types to base 2, 3, 5, 8, 9, and beyond.

The purpose of this exercise is to show the Mathletes that explorations or passions of mathematical discoveries can produce remarkable results. The repeated division reinforces division, multiplication, subtraction and audition, while reinforcing the translation of decimal numbers into any base.

Some of my Mathletes even committed to baking actual cakes with icing that would resemble a division problem in tiers to show the cake method.

I hope you enjoy this exploration as much as I did as a child and still do as an educator.