How to make BigDecimal division more precise

I'm having an issue with BigDecimals, the simplified idea is to:

• define a value for the total
• split the total in 3 parts defined by weights, these weights are 3 double values that add up to 100.0
• sum up the parts
• the sum should be close to the total, the error should be at most 0.00000001

Here's the failing test:

    @Test
    fun sanityCheckExampleForStackOverflow() {
        val whole = BigDecimal.valueOf(2_000_000_000.00)
        val weights = listOf("25.453778250984232", "35.38647064849812", "39.15975110051765").map { BigDecimal(it) }

        val parts = weights.map { weight ->
            // w / 100 * total
            weight.divide(BigDecimal(100)).times(whole)
        }

        val sumOfParts = parts[0] + parts[1] + parts[2]
        val difference = sumOfParts - whole

        assertTrue(difference <= BigDecimal("0.00000001"))
    }

What's missing?

Given your weights sum to 100.000000000000002, the value of sumOfParts is 2000000000.000000040, which is 0.00000004 from your original value, which is four times bigger than the desired difference of 0.00000001.