# Stupid math question about unit conversion accuracy / percision. **URL:** \ **Category:** Factual Questions\ **Created:** [August 15, 2007, 9:09pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733 "2007-08-15T21:09:20Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![Emilio\_Lizardo](https://avatars.discourse-cdn.com/v4/letter/e/898d66/32.png) [@Emilio\_Lizardo](https://boards.straightdope.com/u/Emilio_Lizardo)\ **Post date:** [August 15, 2007, 9:09pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/1 "2007-08-15T21:09:20Z")
I was browsing the local real estate listings, and I happened to notice something that caught my eye. To whit, the ‘lot size’ of one property was listed in acres, out to _17 freaking decimal places!_ Now I’m no surveyor, but it seems unlikely that the lot has been measured THAT accurately. Presumably someone converted from square feet and didn’t truncate properly. That being said, how do I convert that number into units that would correctly express that much accuracy? What unit is 1/10[SUP]17[/SUP] of an acre? Square microns? Maybe it would be easier to do in metric. ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [August 15, 2007, 9:13pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/2 "2007-08-15T21:13:12Z")
It’s about the area of a square with sides of 0.000008 inch ---
**Author:** ![futurebird](https://avatars.discourse-cdn.com/v4/letter/f/7cd45c/32.png) [@futurebird](https://boards.straightdope.com/u/futurebird)\ **Post date:** [August 15, 2007, 9:14pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/3 "2007-08-15T21:14:49Z")
Carpenters hate it but you CAN use decimals for feet. ie. 1.3 feet or 1.56 feet that is 1 foot 56/100 feet or 1’ and 14/25 feet am I helping? ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [August 15, 2007, 9:18pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/4 "2007-08-15T21:18:26Z")
Well, it’s about 62.7_10[sup]-12[/sup] square inches, or 40.5 femtometers squared (10[sup]-15[/sup]), or if you don’t like working with such small numbers, 4.05_10[sup]6[/sup] Angstroms squared. Take your pick. ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [August 15, 2007, 9:19pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/5 "2007-08-15T21:19:22Z")
I get an acre is about 4047 square meters or a little over 4\*10[sup]9[/sup] mm[sup]2[/sup] Going to microns brings us to 4\*10[sup]15[/sup] square microns. Yeah, I don’t buy it, either. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [August 15, 2007, 11:41pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/6 "2007-08-15T23:41:27Z")
Either it’s a typo, or some realtor is confusing “more precision” with “more accuracy”. ---
**Author:** ![illoe](https://avatars.discourse-cdn.com/v4/letter/i/a3d4f5/32.png) [@illoe](https://boards.straightdope.com/u/illoe)\ **Post date:** [August 16, 2007, 4:27am UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/7 "2007-08-16T04:27:51Z")
Judging only by the spelling in many real estate ads, confusing Realtors[sup]TM[/sup] is as easy as falling off a roof, puffed up by “pride of ownership.” ---
**Author:** ![Monty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/monty/32/47_2.png) [@Monty](https://boards.straightdope.com/u/Monty)\ **Post date:** [August 16, 2007, 4:53am UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/8 "2007-08-16T04:53:35Z")
[QUOTE=futurebird] Carpenters hate it but you CAN use decimals for feet. ie. 1.3 feet or 1.56 feet that is 1 foot 56/100 feet or 1’ and 14/25 feet am I helping? [/QUOTE] Wouldn’t a professional carpenter be familiar with an Engineer’s Rule, which has one scale dividing feet into 10ths, 100ths, etc.? ---
**Author:** ![Civil\_Guy](https://avatars.discourse-cdn.com/v4/letter/c/d78d45/32.png) [@Civil\_Guy](https://boards.straightdope.com/u/Civil_Guy)\ **Post date:** [August 16, 2007, 5:50am UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/9 "2007-08-16T05:50:26Z")
Not sure if this is to the point of the the OP, but try this: For any conversion, keep the same number of non-zero leading numbers as in the original value, to maintain relative precision - if a zero is bracketed by other numbers, count that towards precision. For example, if you’re told that something is 400 m away, that’s only one digit of precision - so to convert to feet, figure it’s no more precise than saying that it’s 1,000 feet away. No, this example isn’t very precise under either measurement system - that’s the point here. If you’re told that the survey lot is 6,324.7 square meters, you can figure that that’s about the same as saying 68,079 square feet or 1.5629 acres. Which brings out the other point: if you just don’t need the precision for the purpose at hand, forget it - it just suggests lack of sensibility. ---
**Author:** ![flight](https://avatars.discourse-cdn.com/v4/letter/f/bbce88/32.png) [@flight](https://boards.straightdope.com/u/flight)\ **Post date:** [August 16, 2007, 1:37pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/10 "2007-08-16T13:37:02Z")
[QUOTE=Civil Guy] Not sure if this is to the point of the the OP, but try this: For any conversion, keep the same number of non-zero leading numbers as in the original value, to maintain relative precision - if a zero is bracketed by other numbers, count that towards precision. For example, if you’re told that something is 400 m away, that’s only one digit of precision - so to convert to feet, figure it’s no more precise than saying that it’s 1,000 feet away. No, this example isn’t very precise under either measurement system - that’s the point here. If you’re told that the survey lot is 6,324.7 square meters, you can figure that that’s about the same as saying 68,079 square feet or 1.5629 acres. Which brings out the other point: if you just don’t need the precision for the purpose at hand, forget it - it just suggests lack of sensibility. [/QUOTE] Note, if you measure something and it comes to 400m exactly (plus or minus half a meter), you would express this by putting a bar over the zeros, showing that they are significant. Also, note that if you measured it to 400m (plus or minus .05 meters), you would write 400.0m. Any zeros after the decimal are automatically significant. Preserving accuracy is a big problem these days as calculators and computers make it just as easy to get an answer with a dozen digits as one with three. Thus, people tend to include the extra digits thinking they are being more accurate, when in fact they are transferring _less_ information. You have lost the understanding of how accurate your original measurement was. Note also that the rules **Civil Guy** quotes are for multiplication and division only. For addition and subtraction you base the answer on the actual digit location, not the number of significant digits. Examples: For multiplication, keep only the number of significant digits in your least accurate measurement. 101\*.4=50 101\*.40=50(with a little bar over the zero) 101\*.400=50.5 Far addition, keep only the place of your least accurate measurement 100+4=100 110+4=110 111+4=115 ---
**Author:** ![flex727](https://avatars.discourse-cdn.com/v4/letter/f/258eb7/32.png) [@flex727](https://boards.straightdope.com/u/flex727)\ **Post date:** [August 16, 2007, 3:22pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/11 "2007-08-16T15:22:08Z")
I work in a very high tech industry that has metrology tools to measure very thin films in the range of 10 angstroms to 10 microns. You would think that with all the thought that must go into the design and manufacture of these tools that more thought would go into the precision of the data outputed, but no, this machine always reports film thicknesses to 4 decimal places even when the unit is angstroms (e.g. 4,123.8497 ang). A single silicon dioxide molecule, of which this film might be composed, is many angstroms in diameter. 1/10,000th of an angstrom, in this context, is quite meaningless. ---
**Author:** ![Plynck](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Plynck](https://boards.straightdope.com/u/Plynck)\ **Post date:** [August 16, 2007, 9:08pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/12 "2007-08-16T21:08:50Z")
[QUOTE=Emilio Lizardo] Now I’m no surveyor, but it seems unlikely that the lot has been measured THAT accurately. [/QUOTE] Actually, it’s entirely possible that it has. If it is a subdivided lot, the surveyor/engineer would have divided the original property into smaller lots, using required frontages, setback, minimum acreages, etc. As a result, these new property lines may have very precise bearings (such as N-27d-31m-42s), and distances (310.67’). These can be mathematically calculated into square feet, and divided by 43,560 to give an extremely precise acreage. And completely worthless, as stated above. Any measure using acreage is usually for municipal purposes (such as determining taxes or drainage areas for storm drainage control) or for real estate transactions, and anything carried to more than hundredths (two decimal places) is pointless. It really depends, too, on where you live. Rounding off the area of a Texas cattle ranch to anything less than one hundred might seem ludicrous, whereas my lot (0.15 acres) would matter a great deal to me (or more accurately my neighbor) if it were to be rounded up to the nearest tenth. 🙂 ---
**Author:** ![Tim\_T-Bonham.net](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tim\_T-Bonham.net](https://boards.straightdope.com/u/Tim_T-Bonham.net)\ **Post date:** [August 16, 2007, 10:31pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/13 "2007-08-16T22:31:09Z")
[QUOTE=Monty] Wouldn’t a professional carpenter be familiar with an Engineer’s Rule, which has one scale dividing feet into 10ths, 100ths, etc.? [/QUOTE] No. Absolutely not. And any carpenter who did happen to be familiar with it would refuse to use such a thing. Carpenters are very traditional. My uncle, who was a professional carpenter all his life, did know about the meter & metrical system of measurements. But he refused to recognize them. If anyone ever said anything about a meter on any of his construction sites, he would send them to the back of the building, where the power company had installed the electrical meter. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [August 17, 2007, 1:32am UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/14 "2007-08-17T01:32:56Z")
I understand that using Pi = 3.1416 is good enough for all practical purposes. [A value truncated to 39 decimal places is sufficient to compute the circumference of the visible universe to a precision comparable to the size of a hydrogen atom…](http://en.wikipedia.org/wiki/Pi) I would consider the last 15 decimal places given on the property a waste of time - and evidence of inability to proofread :eek: . ---
**Author:** ![DesertDog](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desertdog/32/11503_2.png) [@DesertDog](https://boards.straightdope.com/u/DesertDog)\ **Post date:** [August 17, 2007, 3:27pm UTC](https://boards.straightdope.com/t/stupid-math-question-about-unit-conversion-accuracy-percision/415733/15 "2007-08-17T15:27:09Z")
When I was small, I heard a story about measuring the height of Mount Everest and [Wiki](http://en.wikipedia.org/wiki/Mount_everest#Measurement) confirms it: > [@Wikipedia](#): > > Radhanath Sikdar, an Indian mathematician and surveyor from Bengal, was the first to identify Everest as the world’s highest peak in 1852, using trigonometric calculations based on measurements of “Peak XV” (as it was then known) made with theodolites from 240 km (150 miles) away in India. Measurement could not be made from closer due to a lack of access to Nepal. “Peak XV” was found to be exactly 29,000 feet (8,839 m) high, but was publicly declared to be 29,002 feet (8,840 m). The arbitrary addition of 2 feet (0.6 m) was to avoid the impression that an exact height of 29,000 feet was nothing more than a rounded estimate. Notice in the third paragraph, one meter of snow depth is rounded to ‘3 ft’ not 3 ft, 3.39 in – entirely reasonable.