You are correct that Debt-to-GDP is not dimensionless, but the ratio is a common comparison in evaluating national finances. It has units of time: $ / ($/year)

You are correct that Debt-to-GDP is not dimensionless, but the ratio is a common comparison in evaluating national finances. It has units of time: $ / ($/year) = years of full GDP required to pay off the debt. Similarly power-to-mass ratio is not dimensionless, but it is useful to know the possible acceleration. Think of Debt-to-GDP > 1 year as "credit card debt exceeds annual salary". Yes, credit card debt is $, and salary is $/year, and exceeding 1 is not a particular tipping point, but lower values are better than higher.