The first sentence in Your last statement in your conversation to your daughter is profoundly wrong. Your daughter was not in any way made to better understand fractions by this interaction. By the way, .3333 is a rational number and therefore equal to a fraction.
Your idea did not translate into English. I think you are trying to say that most decimals we see in real life are approximations, not exact measurements, while fractions are exact?
For example I taught my daughter factions this way.
Me: "These factions you see them? Now see these decimal points?"
Her: "Yeah I hate factions they are stupid!"
Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333."
Her: "I always thought it was the otehr way around."