Well,
I was thinking about asking the Department of the Treasury for some help this semester in explaining exactly what 4.5 billion years looks like. They seem to have no problems with really large numbers. Here is a link to a story about the national debt clock being out of room.
Perhaps scientific notation will help? How many significant digits do you want?
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Here's a way to get at deep time that I've been using for years with some success with middle-school aged kids (excerpt from this post). "I cannot in a meaningful way grasp the magnitude of 4.6 billion years, but I can relate it to other periods of time that are meaningful to me. For example, there are approximately 31.5 million seconds in a year. So if I could live one second for every year the earth has existed, I would survive about 146 years. All of human history (the last 10,000 years) would pass in the last 2 hours and 47 minutes of my life."
Tell the students we're going to create a time machine that goes back at the rate of one year for every second in the classroom, have them brainstorm events. Assign ages (at least roughly). People tend to think in terms of wars and other historical events, so (e.g.), the Vietnam conflict ended 34 years ago, the Revolutionary War was 232 years ago. Make a table of suggested events on the board/overhead, and simply use seconds for years. When doing this with kids, I have everyone stand up to begin with. When I close the door, the time machine "starts," and we count seconds backwards. Students sit when we reach their age (with middle schoolers, only a few seconds). I cross out each event as we "pass it."
The point that becomes clear is that most historical events we think of from a human context are gone in a few minutes; even "distant" events like the birth of Jesus, or the building of the pyramids, pass in an hour or so. The glaciers receded less than three hours ago. Most geological events require weeks or years to get to. This does not get at the "how do we know" question, but seems to get to kids at least a sense of the vastness of geo-time.
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