This answer depends a bit on your age, the types of activities you partake in and the kind of work you do/are planning to do but here goes:
I am thinking of some uses of fractions where decimals are not typically used. One might be cooking. Often the ingredients (1/2 cup of four and so on) are measured using fractions. If you were in a world with decimals you might need to make (1/3) the servings of a recipe that calls for 1/4 of a cup of some ingredient and instead of 1/12 have to deal with a long repeating decimal that probably would need to be approximated so would not be precise.
While on the subject of food ordering pizza (1/2 with pepperoni, 1/4 mushrooms and 1/4 plain) would be doable after you got used to it but probably not as comfortable. Dividing up slices of pizza among friends (one slice is usually 1/8 of a pie) might be awkward though eventually doable.
Estimation - the biggest issue is exactitude versus estimation. When we use a fraction like 1/3 that is an exact value, but when we use .333 or .3333333 no matter how many 3s we use we are only estimating because the 3s go on forever and we can't write them forever. Yes, we can use .3 (with a bar over the 3, but now try to multiply that with .456565656 with a bar over the 56. This becomes practically impossible unless we estimate ... so the biggest issue would be that you would lose precision in many calculations and measurements and have to deal with answers that are good enough (but not exact).
Now say you work on some major car company or you design bridges or you are a scientist developing medicine that cures diseases, would not you want the ability to measure and compute precisely? If I split the pizza up wrong it is not a big deal. If I use a little more flour or a little less than I should in the recipe it might not make much of a difference in the end but if I am doing something that impacts the health, safety or well being of another human being, I would not want to live in a world where I have to estimate and can't count on having the exact, precise value.
