Split a value x ways

[M-Lewinski]

tl;dr How to split value x ways correctly?

Disclaimer: personally I always try to first look for information and details about specific subjects before asking. I hope that this issue may help other people like me who try to move from shopspring/decimal to a library with better performance.

Problem, I’m currently facing is splitting number X ways. For example if we have value 100 that has to be split between 3 entities:
I will have to give two of them 33.33333 and one of them will receive the remainder which is 33.33334. After adding all the values together I will get the base value which is 100.

I understand that representing fractions of value would sometimes require an infinite amount of memory but it’s possible to do this with specified precision which for library shopspring/decimal is 16.

Here is the example code of splitting value x ways:

package main

import (
	"fmt"
	"github.com/shopspring/decimal"
)

func split(value, number int) (decimal.Decimal, decimal.Decimal){
	baseValue := decimal.NewFromInt(int64(value))
	num := decimal.NewFromInt(int64(number))
	lower := baseValue.Div(num)
	higher := lower.Mul(num)
	higher = baseValue.Sub(higher).Add(lower)
	return higher, lower
}

func check(higher, lower decimal.Decimal, number int) decimal.Decimal{
	baseValue := decimal.Zero
	for i := 1 ; i < number ; i++ {
		baseValue = baseValue.Add(lower)
	}
	baseValue = baseValue.Add(higher)
	return baseValue
}
func main(){
	baseValue := 100
	number := 13
	higher, lower := split(baseValue,number)
	baseValue2 := check(higher,lower,number)
	if baseValue2.Equal(decimal.NewFromInt(int64(baseValue))){
		fmt.Println("Correct")
	} else {
		fmt.Println("Incorrect")
	}
}

So far above code always return correct values for most of my test cases.

Creating similar code with this library will return correct results for values like 100 split 3 ways. But for example 100 split 13 ways will return a value of 99.9999… .
Is it possible to achieve the same results using this decimal library?