Editing 1047: Approximations

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"Lots of emails mention the physicist favourite, 1 year = pi × 10⁷ seconds. 75⁴ is a hair more accurate, but it's hard to top 3,141,592's elegance." π × 10⁷ is nearly equal to 31,415,926.536, and 75⁴ is exactly 31,640,625. Randall's elegance belongs to the number π, but it should be multiplied by the factor of ten.

Using the traditional definitions that a second is 1/60 of a minute, a minute is 1/60 of an hour, and an hour is 1/24 of a day, a 365-day common year is exactly 31,536,000 seconds (the "''Rent'' method" approximation) and the 366-day leap year is 31,622,400 seconds. Until the calendar was reformed by Pope Gregory, there was one leap year every four years, making the average year 365.25 days, or 31,557,600 seconds. On the current calendar system, there are only 97 leap years in every 400 years, making the average year 365.2425 days, or 31,556,952 seconds. In technical usage, a "second" is now defined based on physical constants, even though the length of a day varies inversely with the changing angular velocity of the earth.  To keep the official time synchronized with the rotation of the earth, a "leap second" is occasionally added, resulting in a slightly longer year.

|align="left"|"''Rent'' Method" refers to the song "{{w|Seasons of Love}}" from the musical ''{{w|Rent (musical)|Rent}}''. The song asks, "How do you measure a year?" One line says "525,600 minutes" while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.

|align="left"|The {{w|fine structure constant}} indicates the strength of electromagnetism. It is unitless and around 0.007297, close to 1/137. The joke here is that Randall chose to write 140 as the denominator when 137 is much closer to reality and has just as many digits (although 137 is a less "round" number than 140, and Randall writes in the table that he's "had enough" of it).  At one point the fine structure constant was believed to be exactly the reciprocal of 137, and many people have tried to find a simple formula explaining this (with a pinch of {{w|numerology}} thrown in at times), including the infamous {{w|Arthur Eddington|Sir Arthur "Adding-One" Eddington}} who argued very strenuously that the fine structure constant "should" be 1/136 when that was what the best measurements suggested, and then argued just as strenuously for 1/137 a few years later as measurements improved.

|align="left"|Either [[Randall Munroe]] is friends with the President or he works for 9/11 .

|align="left"|Grows by 3 million each year. As of 2024, the actual number is ~17 million smaller.

|align="left"|A U.S. liquid gallon is defined by law as 231 cubic inches

|align="left"|Standard gravity, or standard acceleration due to free fall is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s², which is exactly 35.30394 km/h/s (about 32.174 ft/s², or 21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from the rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5 per cent greater at the poles than at the equator.

Randall used the letter ''g'' without a suffix, which can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth.