Amazon's safe handling of your credit card information is important for everyone but especially businesses since Amazon doesn't permit business checking accounts as payment options (Reference 1). Since this might mean that you'll be using your business credit card that much more, the concern is not only protecting your financial information that's stored with Amazon, but keeping information safe when you actually make a purchase.
As long as you do your part to keep you Amazon account safe, such as by creating a strong password, Amazon says it'll do its part to protect your financial information — even referring to your account security as a "right" (Reference 2). At the point of sale, Amazon employs multiple methods to keep your credit card data safe. One method is an authorization process in which Amazon communicates directly with your credit card issuer to verify that the card is valid and hasn't been reported stolen.
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Another method Amazon employs is Secure Sockets Layer (SSL) technology that encrypts information sent over the Internet when you make an Amazon purchase. The aim is that even if someone intercepts your information it will be indecipherable and unable to use. Also, when you confirm an order on the Amazon site, only the last four digits of your credit card appear on the screen to prevent snoopers from getting your information (References 3 and 4).
Alternative Payment Support
Amazon also supports a separate payment method that functions like its own version of PayPal: Amazon Payments. With this service, you can add your credit card or checking account — even a business checking account — to your Amazon Payments profile, and purchase from any website that accepts Amazon Payments. This payment method also utilizes SSL technology to encrypt any financial information used when making a purchase (References 7 and 8).
Doing Your Part
Beyond creating a secure password, Amazon asks that you take other preventive measures to keep your credit card data safe. For example, if you make a purchase using a computer that others have access to, be sure to log out of your Amazon account when you're finished. Additionally, never send your credit card information to anyone in an email, since this is likely not encrypted and therefor unsafe (References 5 and 9).