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I'm wondering if anyone knows where the apps that can show you where the nearest petrol station is etc get their data from?

There must be some data that connects a lot of businesses to a specific geolocation.

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Take a look at http://compass.webservius.com Data on 16+ million businesses in the US, including industry classification (e.g. gas satation) and latitude/longitude coordinates, all in a REST API form.

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There is no universal lookup source for this.

Those sites all have access to some sort of directory - from something like the yellow pages, from the petrol station chains themselves (most likely), or entered manually by staff or other users.

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