How thin is our atmosphere relative to the size of Earth? According to the GRC NASA website, Earth's atmosphere is a thin sheet of air extending from the surface of the Earth to the edge of space. Some videos on youtube also point out that if the Earth is the size of an apple, its atmosphere is just as thick as the apple's skin. But when we look at some diagrams, Earth's atmosphere is thick. For instance, when someone says that the atmosphere is a thin sheet of air, does he/she take in to account the thick layer thermosphere or exosphere? Or is it just that the diagrams we commonly see have inaccurate visual representation?
The answer to your question depends on where one defines the edge of the atmosphere.
The Earth's atmosphere is layered. The thickness, density of composition of each layer varies. The five layers are:

Exosphere: 700 to 10,000 km (440 to 6,200 miles)
Thermosphere: 80 to 700 km (50 to 440 miles)
Mesosphere: 50 to 80 km (31 to 50 miles)
Stratosphere: 12 to 50 km (7 to 31 miles)
Troposphere: 0 to 12 km (0 to 7 miles)

Being the outermost layer, the exosphere is the layer with the most nebulous upper boundary. It is also the layer with the lowest density and it is primarily composed of very low density hydrogen and helium, particularly in the outer/upper reaches.
Because of the low density of the exosphere and also because the Karman Line, which is 100 km above the Earth, which the line designated where Earth ends and outer space begins, the exosphere is sometimes ignored.
So if one accepts the top of the Thermosphere as being the effective upper boundary of the atmosphere the effective thickness of the atmosphere is only 700 km compared the radius of the Earth, which is 6370 km.