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Deciliters measure volume, while grams measure mass, so they aren't equivalent. However, if you are measuring water, one milliliter is exactly one gram, so .01 deciliters of water would be equivalent to one gram of water. This conversion only works with water, though.
1 decilitre is 100 millilitres, which is about 3.38 U.S. fluid ounces, or 0.423 U.S. cups. (Note: 1 U.S. cup = 8 U.S. fl. oz.)
In Imperial fluid measure, 1 decilitre is about 3.51 Imperial fluid ounces, or 0.352 Imperial cups. (Note: 1 Imperial cup = 10 Imperial fl. oz.)
A "metric cup" is defined as 250 millilitres, so 1 decilitre is exactly 0.4 metric cups.