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The "karat" is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of gold in a 20.0 karat gold necklace whose weight is 1.09 N?

The sequence here is..

The implication in the question is to find out how much of the weight is gold, so do this using the fraction given.

Convert the weight to mass using F=ma and I would use a=9.8 m s^-2 unless your question/text book has a different value.

Now convert the mass to volume using density=mass/volume. The density of gold you will need to get from a data book, wikipedia, or maybe it is in the question/text book.

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