The news has been inundated lately with stories involving vast sums of money, often leading to confusion. As is frequently the case, many in the media and the public have displayed an unfortunate lack of understanding regarding numbers of this size. In this morning's newscast, a commentator said 7 billion was ten percent of seven trillion. As many do, he believed that a trillion is ten times more than a billion. Having been a mathematics professor, I've encountered this many times before. Let's start by defining terms. Outside of the US, the names change, but the principle remains the same. Each named group is a thousand times the preceding one. One million (1,000,000) is 1000 times one thousand. A billion is a thousand million, and a trillion is a thousand billion. I'm sure many of you know this, but the rest of this article will give you great ways to explain it to those who may not. Here's a relatable way to understand these large numbers. Imagine a thousand seconds, which is just 16 minutes and 40 seconds. A million seconds is a thousand times longer, roughly 11 days and 14 hours. A billion seconds is a thousand times longer than that, about 31 2/3 years. And a trillion seconds is a thousand times larger than a billion, a staggering 31,689 years. To put it another way, a trillion is a million million. The news has been filled with discussions about government spending and debt lately. The 2024 US budget was 6.75 trillion. If we were to measure this in seconds, it would be 213,901 years. The US national debt is 36 trillion, which in seconds equals 1,140,804 years. So, if we were to pay off the national debt at one dollar per second, it would take over a million years. Let's take another example to make these numbers more relatable. A thousand inches is just 83 feet 4 inches, a manageable distance. But a million inches, a thousand times larger, is a whopping 15.78 miles, a five or six-hour hike. Now, a billion inches, multiplying by a thousand again, is 15,780 thousand miles, about 2/3 of the distance around the Earth. And a trillion inches? That's a thousand times farther, 15,780,000 miles, about halfway to the planet Venus. Now, let's put these distances into a financial context. The 6.75 trillion dollar national budget, expressed in inches, is farther than the distance to the sun. And the $36,000,000,000,000 national debt, measured in inches, is 568,080,000, somewhat farther than the distance to Jupiter. It takes light, the fastest thing there is, about 51 minutes to travel that far. That's a long way to go! Here's another example. A thousand dollars would be enough to give everyone on Earth 1/180000 of a cent or 3/10000 of a cent to every American. A million dollars could provide 1/80 of a cent to everyone on Earth or .3 cents to every American. A billion dollars would be enough to give everyone on Earth 12.5 cents, or all Americans $2.86. A trillion dollars would provide everyone on earth $125, or every American $2857. The US budget would be enough to give everyone on earth $875, or each American $20,000. Finally, the US national debt, 36,000,000,000,000, could provide each person on Earth $4500, or every American $102,852. Of course, since it's a debt, that's not what each American gets; it's what they owe. Let's try another one. A movie is composed of thousands of still pictures shown one after the other. It shows these pictures, called frames, at a rate of 24 frames every second. A thousand frames would take 41 2/3 seconds. Watching a movie with a million frames would take 11.57 hours. To watch a film of a billion frames, you'd have to commit to 1 year and four months of watching. A movie of a trillion frames would take 1,320 years to watch. The US budget of 6.75 trillion, made into a movie with a frame for every dollar, would take 534,751 years to watch. And a film with 36 trillion frames would take 2,852,005 years to watch. Finally, let's use a more lighthearted example: the weight of ants. An ant weighs a mere .004 grams. A thousand of these little picnic guests would weigh 4 grams—about four standard paper clips. A million ants would weigh about 4 kilograms or 1.818 pounds. A billion ants would weigh 4000 kg, nearly a ton, and outweigh ten human picnickers. A trillion ants would weigh 1,818,181.8 kg, almost 1000 tons. The national budget, expressed in ant weights, would be 27,000,000 kg. or 6136.4 tons. The national debt would weigh 144,000,000 kg or 65,454,545.45 lbs or 32727 tons, which is about the weight of the human population of Atlanta, Georgia. That's a big picnic! Understanding large numbers is essential to understanding the world. The natural world and our civilization involve large numbers beyond comprehension without some context. In my time teaching math, I've used examples like this many times, but every time I do, I am amazed. You may find that if you re-read this article, you have the same experience. I've re-read it several times—proofreading it—and my appreciation for the size of these numbers never dims. If you have examples of your own to share, you're welcome to add them in the comments section below.

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