How do you do 36 with the base of 6?

Answer 1

The answer is 100.

(Important note: To understand this answer you need to understand how a number is made up (what the digits actually mean). To do this, you need to be familiar with the concept of powers. I will give you the answer and explain what the digits in the number mean, but if you are not comfortable with powers of numbers then you will need to research this further yourself.)

Ok!

The number 36 in base 10 (which is the decimal system we all commonly use) means (from right to left):

(6 * 100) + (3 * 101) = (6 * 1) + (3 * 10) = 6 + 30 = 36.

In base 10, there are 10 possible digits (0 to 9) and each digit in a number is a multiple of a power of 10. 100 equals 1 (any number to the power 0 equals 1), and 101 equals 10.

In base 6 there are now only 6 possible digits (0 to 5) and this time they are going to be representing multiples of powers of 6.

So let us consider what the powers of 6 are.

60 = 1 (remember anything to the power 0 = 1)

61 = 6

62 = 6 * 6 = 36

Luckily for us this question is going to be straightforward then as 62 = 36 (the number we are after!)

If we were trying to write 100 (i.e. 102) in base 10 we would, of course, just write it as 100 because this means [from right to left] (0 * 100) + (0 * 101) + (1 * 102) = 0 + 0 + 100 = 100. For this reason, in decimal 100 is the same as 102.

So, in exactly the same way, we can write the number 36 in base 6 as 100 because now the number means (0 * 60) + (0 * 61) + (1 * 62) = 0 + 0 + 36 = 36! You should hopefully now see that this is because 100 is now the same as 62 (36) rather than 102.