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Density isn't determined by the size of the specimen but by its mass per unit of volume. An oak branch has the same density as the whole tree it came from--the weights are vastly different, but density is the same.
It depends on what he whole is. It should be obvious that the size of a whole proton will be very very small whereas the size of the universe will be incredibly big.
Fractions that have the same size or the same value are called equivalent fractions. They represent the same amount or quantity, even though they may look different. For example, 1/2 and 2/4 are equivalent fractions because they both represent half of a whole.
Having the same size and shape means that you look the same height and size.
Yes, they can be put into a one-to-one correspondence. The size of both sets is what's called a "countable infinity".