In 2005, Apple introduced electronic receipts at its stylish retail stores. More mainstream retailers found the checkout system difficult to replicate and, Ms. Miles said, worried that most shoppers were not quite ready for such a technological leap.

Now, though, the rush to imitate Apple’s success is in full force, and paperless receipts have become a rite of passage for retailers trying to integrate the digital experience into their brick and mortar stores.

Ms. Sock said that once cellphones were widely used for payments, as with Google Wallet and other efforts, e-receipts would become standard. “A lot of these retailers are looking into mobile payments, and with mobile payments, you have to talk about the digital receipt,” she said.

This year, Nordstrom introduced devices in many of its stores so roving clerks could check out shoppers on the spot. The devices can print receipts via wireless Internet when a customer asks, but the goal is to provide digital receipts.

“As the technology has started to evolve, we saw the opportunity to create a better experience for the customer, wherever they are in a store,” said Jamie Nordstrom, president of Nordstrom’s direct-sales division. “A customer’s in a dressing room, they try on a bunch of things, they say, ‘I want to buy this and that.’ Now, we’ve got to take them out of the dressing room, wrap all that stuff at the wrap desk, use the cash register somewhere else.”

Mr. Nordstrom said Nordstrom was also thinking about ways to make its e-receipts more appealing, perhaps by adding a picture of the item to the receipt so a shopper could post it to a Facebook wall.

Beyond the cost savings and environmental benefit (an estimated 9.6 million trees are cut each year for receipts in the United States, according to allEtronic, a digital receipt company), the e-receipts present marketing opportunities for retailers. Gap, Nordstrom and many other stores, for example, add the customer’s e-mail address to a mailing list for follow-up offers.