How many light years away from the Sun are we?

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Well, you could look up the numbers easily enough: The astronomical unit (the average distance between the Earth and the Sun) is defined as exactly 149,597,870,700 meters, whereas the light year is defined as the distance covered by light in a Julian year (365.25 days), which means exactly 9,460,730,472,580,800 meters. The rest is a simple division.

But instead of typing 149597870700/9460730472580800 into Google for you (yes, Google can serve as your calculator) let me show you how you can estimate the answer to this question reasonably accurately without looking up anything or using any calculator, so long as you remember two useful numbers.

It is not hard to remember that the Earth-Sun distance is roughly 150 billion meters; that is, the digits 15 are followed by 10 zeroes.

It is also not too hard to remember that a light year is roughly 10,000 trillion meters; that is, the digit 1 is followed by 16 zeroes.

So 15 followed by 10 zeroes divided by 1 followed by 16 zeroes… that’s the same as 15 followed by no zeroes at all divided by 1 followed by 6 zeroes; or 15 parts in a million. And that answer is correct within about 5.5%.

The error is due mainly to the fact that the light year is overestimated by more than 5%, so we underestimated the ratio. “Boosting” that 15 parts in a million by an extra 5% gives 15.8 parts in a million, which is actually quite accurate. But at this point, you’re probably better off using a calculator after all.