One metre is exactly 1,000 millimetres. This is the working conversion of engineering and construction, where the metre states the overall size and the millimetre states every detail on the same drawing.
About the units
The millimetre is a thousandth of a metre, from the Latin mille. It is the smallest unit most people encounter physically — the divisions on an ordinary ruler — and it is small enough that ordinary manufacturing tolerances can be expressed in whole numbers or simple decimals of it. That is precisely why technical drawing adopted it. In metric engineering practice, dimensions on a drawing are given in millimetres without any unit marked at all, a convention so widespread that writing "mm" after each number reads as amateurish. The metre remains the SI base unit, and the millimetre is simply that unit with a prefix.
The exact factor
The factor is exactly 1,000: shift the decimal point three places. 2.4 m is 2,400 mm; 0.075 m is 75 mm; 18,500 mm is 18.5 m. The relationship to the centimetre is worth holding alongside it, because mixing the two is the classic metric error: 1 cm is 10 mm, so a measurement of 45 mm is 4.5 cm and 0.045 m. Three units, one number, three different decimal positions.
Where you meet this conversion
Any technical drawing is the primary case. Architectural plans give overall building dimensions in metres and every window, door and wall thickness in millimetres. Machining, sheet metal work, cabinetmaking and 3D printing all specify in millimetres while the finished object is described in metres. Rainfall and snowfall are measured in millimetres, and a report of 25 mm of rain over a day is 0.025 m spread across an area — the depth is small, but multiplied by a roof or a field it becomes tonnes of water.