The thing that makes this problem tricky is the baby is weighed in pounds while the dosage is given in metric.
So first convert the weight of the baby.
1kg = 2.2 lb
change that into a useful conversion factor by dividing both sides by 2.2 lb.
1kg / 2.2 lb = 1
Now multiply that conversion factor times the 17 pound baby.
1kg / 2.2 lb times 17 lb = 7.72 kg
(note that the lb units cancel)
The dose needed is in mg per kg, so multiply the weight of the baby times dosage
7.72 kg times 10mg/kg = 77.2 mg
(note that the kg units cancel)
So the kid needs 77.2 mg.
The syrup has 100 mg/5ml.
we cant multiply this factor times the baby's weight because we'd have mg squared over ml. So divide by the factor.
division by a factor is the same as multiplying by the inverse.
77.2 mg times 5ml/100 mg = 3.86 ml.
round to 2 decimal places, 3.9 ml.