Not all unit conversions carry the same level of certainty. Some are exact by definition -- there is no measurement error involved, only arithmetic. Others are standardized approximations of something that varies in the real world, and no amount of decimal precision in the calculator fixes that underlying variability.
Exact conversions: physical unit definitions
An inch is defined as exactly 2.54 centimeters, by international agreement -- not measured, not approximated, exactly defined that way. The same is true for most length, area, and volume conversions between metric and imperial units: a mile is exactly 1.609344 kilometers, a pound is exactly 0.45359237 kilograms. These numbers can be extended to as many decimal places as you want with no loss of accuracy, because they are definitions, not measurements.
Approximate conversions: things that vary in reality
A cup of flour in grams is a different story. 'Cup' is a volume, but flour's density depends on how tightly it's packed, whether it's sifted, and even humidity -- so a 'cup of flour equals 120 grams' conversion is a cooking-reference average, not a physical law. The same applies to many cooking-ingredient conversions (rice, sugar, shredded cheese) and to some biological or environmental conversions -- the ratio is a reasonable standard reference, but the real-world value can genuinely differ from one instance to the next.
This is also why a calculator can show a conversion to eight decimal places and still be 'wrong' for your specific cup of flour -- the extra decimal places are precise about the reference ratio, not about your actual ingredient.
How to tell which kind you're looking at
As a rule of thumb: pure physical unit conversions (length, mass, area, volume, energy, data storage) are exact. Anything involving a substance with variable density, a biological measurement, or a real-world process is a standardized approximation. When the result matters for a precise application -- baking a recipe that must turn out exactly right, engineering tolerances -- treat exact unit conversions as reliable to as many digits as you need, and treat approximate ones as a solid starting estimate to verify against your specific material.