The Base 10 Number System you have been familiar with since childhood consists of these two components:
➊ the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
➋ the place values 10⁰, 10¹, 10², 10³, 10⁴, ... or ... in standard form: 1, 10, 100, 1000, 10000, ...
All (whole) numbers can be created with the digits and place values above.
The base 10 number 324 means: (3 x 100) + (2 x 10) + (4 x 1)
The Base 5 Number System you are learning about consists of these two components:
➊ the digits 0, 1, 2, 3, 4
➋ the place values 5⁰, 5¹, 5², 5³, 5⁴, ... or ... in standard form: 1, 5, 25, 125, 625, ...
All (whole) numbers can be created with THESE digits and place values as well.
Converting the (base 10) number 324 means we have to re-construct the number using the new set of digits 0 – 4 and the place values 1, 5, 25, 125, ...
PROCESS:
What is the largest base5 place value that we can divide into 324? 125 you say? Right!
324 ÷ 125 = a quotient of 2 with a remainder 74
What is the largest base5 place value that we can divide into 74? 25 you say? Right again!
74 ÷ 25 = a quotient of 2 with a remainder 24
What is the largest base5 place value that we can divide into 24? 5 you say? Yep!
24 ÷ 5 = a quotient of 4 with a remainder 4
What is the largest base5 place value that we can divide into 4? 1 you say? Terrific!
4 ÷ 1 = a quotient of 4 with a remainder 0
So, 324₁₀ = (2 x 125) + (2 x 25) + ( 4 x 5) + ( 4 x 1)
Now write down all the "quotient" numbers we calculated in the order we found them ...
∴ 324₁₀ = 2244₅ <<< We read this as: "two two four four base 5"
Hope this helps! Cheers! :)
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