To select the set of equivalent decimals, we can analyze each option:
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1.9, 0.19, 0.190 - These numbers are not equivalent, as 1.9 is much larger than both 0.19 and 0.190.
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1.9, 1.09, 1.009 - These numbers are not equivalent, as 1.9 is larger than both 1.09 and 1.009.
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1.9, 1.90, 1.900 - All three of these numbers are equivalent. In decimal form, 1.90 and 1.900 are simply different representations of 1.9.
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1.9, 1.90, 1.090 - These are not all equivalent because, while 1.9 and 1.90 are equivalent, 1.090 is equal to 1.09, which is less than 1.9.
Based on this analysis, the correct answer is 1.9, 1.90, 1.900.