No they’re not. Kilogram is a unit of mass, liter is a unit of volume. They are related to each other by density;
density = mass/volume
Basically, the density measures how “closely packed” the mass of an object is. Bowling balls have around the same volume as basketballs, but we both know they are a lot heavier. That’s because the material used to make bowling balls is very dense (high mass per volume) than a basketball which is mostly filled with air.
The ONLY time mass and volume are numerically equivalent is when the density is 1. Water for example, has a density of ≈1 because 1g fills 1cm³, or 1kg fills 1L. So for water, we can easily calculate mass from volume and vice versa because the density is 1.
You can calculate the density of your bar of soap:
290g/300ml ≈ 0.967 g/ml
Very close to 1, but not quite.
Edit: removed 1kg/m³ because it’s not true
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