One percent is exactly 10,000 parts per million. Both express a ratio rather than an amount, and the choice between them is purely about how many leading zeros you are willing to write.
About the units
A percent is one part in a hundred; a part per million is one in a million. Neither is a unit in the dimensional sense — both are dimensionless ratios — which means they can describe a mass fraction, a volume fraction or a mole fraction, and a figure without that context is incomplete. Air composition in ppm normally means by volume; a contaminant in water in ppm usually means milligrams per litre, which is a mass per volume that happens to coincide with a mass ratio because a litre of water weighs a kilogram. That coincidence is why ppm and mg/l are used interchangeably for dilute aqueous solutions, and why the habit breaks down for anything much denser than water.
The exact factor
The factor is exactly 10,000. Useful equivalents: 1 % is 10,000 ppm, 0.1 % is 1,000 ppm, and 1 ppm is 0.0001 %. Reference values: atmospheric carbon dioxide passed 420 ppm in the early 2020s, which was 0.042 %, and has kept climbing since; the workplace exposure limit for carbon monoxide is around 20 to 35 ppm; and drinking water fluoridation runs at about 0.7 to 1 ppm. Oxygen in air is 20.9 %, which would be 209,000 ppm — a figure nobody writes, which shows where the sensible boundary between the units lies.
Where you meet this conversion
Air quality, water treatment and materials purity. Gas detector alarm thresholds are set in ppm, semiconductor materials are specified to single-digit ppm or below, and alloy composition is given in percent for major constituents and ppm for trace elements. Climate reporting uses ppm for carbon dioxide and ppb for methane and nitrous oxide, which are present in much smaller quantities. Analytical laboratories report in whichever unit keeps the figure between one and a thousand.