One metre is exactly 100 centimetres. Like the other conversions within the metric system this one is a decimal shift rather than a calculation, and there is no rounding involved at any point.
About the units
The centimetre is a hundredth of a metre, from the Latin centum. It is one of the prefixes that survived a deliberate attempt to remove it: the SI system officially prefers prefixes in steps of a thousand — millimetre, metre, kilometre — and the centimetre breaks that pattern. It survived because the alternatives are awkward at human scale. Describing a hand span as 200 millimetres or 0.2 metres is less natural than 20 centimetres, and no amount of standardisation has been able to change that. The centimetre is now firmly established in clothing, body measurement, stationery, cooking and school geometry, while engineering and construction avoid it in favour of millimetres.
The exact factor
The factor is exactly 100: shift the decimal point two places. 1.75 m is 175 cm; 0.4 m is 40 cm; 250 cm is 2.5 m. Because the shift is two places rather than three, this is the metric conversion people most often get wrong by a factor of ten, usually by borrowing the habit from metres and kilometres. A quick check: a person's height in centimetres is a three-digit number, and in metres it has one digit before the decimal point.
Where you meet this conversion
Room dimensions, furniture, luggage size limits and sewing patterns all live in this pair, and airlines are a common source of confusion because cabin baggage limits are published in centimetres while the bags are sold with dimensions in both. In construction the two coexist uneasily: architects work in metres for room sizes and millimetres for details, and centimetres appear mainly on tape measures and in conversation on site.