Will an object with a density of 0.97 g/ml float or sink in water

0.97 g/ml

Since 1000cm³ = 1 litre.  And 1ml = 10^-3 l = 10^-3 * 1000 cm³ = 1cm³ 

0.97 g/ml = 0.97 g/cm³

And since it is less than density of water which is 1.00 g/cm³.   The object will rest on the water.

It will not float. It will float if its density is equal to density of water, and would sink if its density is greater than that of water and would rest on the water if its density is less than that of water.

Matter- occupies space and possesses rest massno matter is the opposite