How Does Step-by-Step on How to Change Bases in Math Work?

Changing bases in math is like switching from one kind of counting system to another, just like how you might count on your fingers or use a ruler.

Imagine you have 10 candies and you want to share them with friends. If you're using base 10 (which is what we usually do), that’s easy: 10 divided by 2 is 5, so each friend gets 5 candies. But what if you’re in a different land where they use base 2, like counting only in ones and twos?

Think of it as changing from your fingers (base 10) to a hand with just two fingers (base 2). In base 2, you count like this:

• 0 = 0 candies
• 1 = 1 candy
• 10 = 2 candies
• 11 = 3 candies
• 100 = 4 candies

So, if you have 10 candies and want to write that in base 2, it becomes 1010, because that means:

• 8 (from the first 1) + 2 (from the second 1) = 10.

It’s like telling your friends how many candies you have, but instead of using ten fingers, you use just two!