One square metre is 10.7639104167 square feet. The awkward figure is the linear conversion squared: a foot is 0.3048 metres, and 0.3048² gives 0.09290304, whose reciprocal is the number above.
About the units
Both units are derived rather than defined: a square metre is the area of a square one metre on a side, and a square foot the area of a square one foot on a side. Since the foot has been exactly 0.3048 m since 1959, the square foot is exactly 0.09290304 m² with no measurement involved. What makes the pair worth a page is not the arithmetic but the intuition gap. People who can convert lengths in their head routinely get areas wrong, because a factor of about 3.28 in length becomes a factor of about 10.76 in area, and nothing about the first number suggests the second.
The exact factor
The derivation is 1 ÷ 0.3048² = 1 ÷ 0.09290304 = 10.7639104167097... The useful mental anchor is that a square metre is a little under eleven square feet. Some reference points: a 20 m² room is 215 ft²; a 1,000 ft² apartment is 92.9 m²; and 100 m² is 1,076 ft². The one to memorise is that 100 m² and 1,000 ft² are roughly comparable, differing by about eight per cent — which is close enough to mislead and far enough to matter in a lease.
Where you meet this conversion
Property listings are the dominant case and the one with money attached. American and British listings quote square feet, the rest of the world quotes square metres, and a buyer comparing across markets who applies the linear factor instead of the areal one will misjudge every property by a factor of three. Construction materials — flooring, tiling, insulation, paint coverage — are sold by area, so an imported product specified in one unit against a room measured in the other needs the conversion done correctly before ordering. Solar panel output, quoted per square metre, is another frequent case.