On Mars a persons weight is 0.4 times the weight on Earth. The gravitational field strength of Earth is 9.8. What is the gravitational field strength of Mars.

Weight = mass x gravitational field strength.

Mass doesn't change when moved around the universe (unless it goes really fast, but that's relativity and way beyond GCSE level!) so if the Weight on mars is 0.4 time that of earth, then the gravitational field strength is also 0.4 times that of earth.

0.4 x 9.8m/s^2 = 3.92 m/s^2

So the gravitational field strength of Mars is around 3.9m/s^2

The formula for the weight is F=mg where g is the gravitational field related to a specific planet. In this case we have that F_{Mars}=0.4F_{Earth}, so replacing we obtain mg_{Mars}=0.4mg_{Earth}, note that the mass is equal everywhere. Dividing both sides by m, we obtain that g_{Mars}=0.4g_{Earth}=0.4x9.8=3.92