Using Ruby, is it possible to print out BigDecimal("1") / BigDecimal("3") as 0.3333333333333... to any length?

You are observing a loss of precision there because you are formatting the BigDecimal object to a Float first (because of your f format flag) which can't represent arbitrary precision floating point numbers.

However, you can use BigDecimal#to_s to format a Bigdecimal object as a string without any loss of precision. Here, the output will use as much precision as is available in the object you are formatting.

When creating your object with BigDecimal#/, it will use some predefined precision, on my box this was 36 on Ruby 3.1. This will result in 36 decimal numbers being printed by default:

result = BigDecimal("1") / BigDecimal("3")
result.precision
# => 36
result.to_s('F')
# => "0.333333333333333333333333333333333333"

If you desire higher precision in the resulting BigDecimal object after your division, you can use BigDecimal#quo instead:

result = BigDecimal("1").quo(BigDecimal("3"), 60)
result.precision
# => 60
result.to_s('F')
# => "0.333333333333333333333333333333333333333333333333333333333333"