1 meter and 89 centimeters
In the SI, one never splits units this way. Either 1.89 m or 189 cm would be correct, 1 meter and 89 centimeters is incorrect.
We'll use 189 cm and note that 2.54 cm = 1 inch exactly,
so 189 cm x 1 inch/2.54 cm = 74.4"
6 feet is 72 inches, so 74.4 - 72 inches = 2.4 inches are leftover. Subtracting 2", 0.4" are leftover. Converting that to a fraction, it is about 13/32, although that is probably more precision than warranted, so the person is 6' 2 13/32", but 6' 2 3/8" may be close enough.