I agree it's bad phrasing, but isn't the only real error here using "with fractions" rather than "with fractional digits"? Perhaps this is an idiomatic differen

I agree it's bad phrasing, but isn't the only real error here using "with fractions" rather than "with fractional digits"? Perhaps this is an idiomatic difference between different English dialects, such as American vs British? I'm not sure. If you read fractions as meaning fractional digits, the inaccuracy goes away completely, I think. I would also use "real number" instead of "real", but that may be more of a stylistic choice rather than idiomatic.