Tenths To Fractions

[DrivingMyk]

Hi everyone!  I'm a resident of Sherman Oaks, California and I vaguely remember moving here from the east as a kid and seeing the "Miles To" signs written in tenths of miles.  Does anyone remember when our Valley freeway signs changed from tenths of miles to fractions of miles?  Any help would be greatly appreciated.  Thanks in advance!

[MarkF]

I remember I-5 in San Clemente used to have some of these signs, which were on a black background, so I'm guessing they were put up pre-1964?

[Gulol]

A stretch of the Ventura Freeway between De Soto and Mulholland Drive had these style signs up (on a black background) until the late 1980s I believe when the freeway was reconstructed through this area and the modern standard signs were erected.

[J N Winkler]

Hi everyone!  I'm a resident of Sherman Oaks, California and I vaguely remember moving here from the east as a kid and seeing the "Miles To" signs written in tenths of miles.  Does anyone remember when our Valley freeway signs changed from tenths of miles to fractions of miles?  Any help would be greatly appreciated.  Thanks in advance!

These are interchange sequence signs, with Caltrans sign spec code G23.  The original G23 spec (issued 1958 or so) featured miles and underlined tenths, with a leading zero for distances under one mile.  In 1959, Caltrans' predecessor agency conformed its signing with the AASHO Interstate signing manual, and as part of these changes, the G23 spec was altered to use vulgar fractions with no leading zero and a straight gutter between whole numbers and fraction rectangles.

Older signs with underlined miles and tenths would have persisted for a considerable length of time since porcelain enamel on steel, which was favored for sign substrates at the time, has a service life of fifty years or more.

[AndyMax25]

Hi everyone!  I'm a resident of Sherman Oaks, California and I vaguely remember moving here from the east as a kid and seeing the "Miles To" signs written in tenths of miles.  Does anyone remember when our Valley freeway signs changed from tenths of miles to fractions of miles?  Any help would be greatly appreciated.  Thanks in advance!

This may have been the sign you are thinking of.

[Atomica]

Hi everyone!  I'm a resident of Sherman Oaks, California and I vaguely remember moving here from the east as a kid and seeing the "Miles To" signs written in tenths of miles.  Does anyone remember when our Valley freeway signs changed from tenths of miles to fractions of miles?  Any help would be greatly appreciated.  Thanks in advance!

This may have been the sign you are thinking of.

I recall seeing that and a number of black overhead signs when I was growing up in the 70s and early 80s myself.  A few streets still had black overheads into the mid-80s.  The last remaining black overhead sign is on the I-5/CA14 truck lanes at the junction of those two highways.  The mileage changeover happened with the sign colour changeover.

[AndyMax25]

I found this pic in my archives. NB what was then CA-7, now I-405 at the Sunset Blvd overcrossing.

[SignGeek101]

This may be a bit of a dumb question, but why was this done? Were fractions just preferred over decimals, or was it something else?

Personally, I think decimals could be more accurate; if the exit is 0.4 miles away, it would most likely be rounded to "road name" ½ instead.

Example:

https://goo.gl/maps/f8hGT

Each of these would have to be rounded.

[mrsman]

This may be a bit of a dumb question, but why was this done? Were fractions just preferred over decimals, or was it something else?

Personally, I think decimals could be more accurate; if the exit is 0.4 miles away, it would most likely be rounded to "road name" ½ instead.

Example:

https://goo.gl/maps/f8hGT

Each of these would have to be rounded.

I think that for most people fractions are more conceptual than decimals.  Especially in the US where we don't have the metric system. 

In my kitchen, I got measuring cups with 1/2 cup, 1/3 cup, 1/4 cup listed as fractions, not decimals.

[SignGeek101]

This may be a bit of a dumb question, but why was this done? Were fractions just preferred over decimals, or was it something else?

Personally, I think decimals could be more accurate; if the exit is 0.4 miles away, it would most likely be rounded to "road name" ½ instead.

Example:

https://goo.gl/maps/f8hGT

Each of these would have to be rounded.

I think that for most people fractions are more conceptual than decimals.  Especially in the US where we don't have the metric system. 

In my kitchen, I got measuring cups with 1/2 cup, 1/3 cup, 1/4 cup listed as fractions, not decimals.

Yeah, I thought it may have had to do with that. Wasn't sure though.

[J N Winkler]

This may be a bit of a dumb question, but why was this done? Were fractions just preferred over decimals, or was it something else?

I think vulgar fractions were chosen for interchange sequence signs for consistency with distance expressions on advance guide signs.  The original edition of the AASHO Interstate signing manual did not have interchange sequence signs, but it did have an example advance guide sign with a vulgar fraction ("Lincoln Ave 1/2 MILE").

Moreover, I think the change was carried out by Caltrans (or, rather, its predecessor agency) on its own initiative, before this signing concept became part of national standards.  The example drawing of an interchange sequence sign that was put in a later edition of the AASHO Interstate signing manual, and then in the 1961 MUTCD, and then in every MUTCD edition thereafter until it was re-mastered for the Millennium edition, was a photoreproduction of the Caltrans G23 specification sheet with vulgar fractions that replaced the original G23 with miles and underlined tenths.

[briantroutman]

Considered one way, tenths make more sense because they correlate to the one decimal place on most car odometers. But in practice, if you're looking down at your odometer to keep track of tenths, particularly on a congested urban freeway, you're probably distracting yourself more than you should.

And I think this gets at why the standard ¹/₂ and ¹/₄ are a better alternative.

For the most part, I don't think people are actually looking at their odometers to see when half or a quarter of a mile has ticked by. Instead, these distances are concepts that motorists are so familiar with, they can relate to them even without measuring the exact distance. Half a mile is about 30 seconds, and a quarter about 15–nice, relatable intervals that motorists can process without taking too many mental cycles away from their driving and environment.

[Road Hog]

Vulgar Fractions would be a great name for a band.

[english si]

Using fractions on road signs is a very Anglophonic way of looking at things. Maybe it's late/non- adoption of the French Imperial Metric system, but it seems to mostly be English-speaking nations that use fractions.

I remember having a discussion with a German who couldn't understand why we didn't use decimals (or better yet, x00 metres). In the end it turned out he learnt fractions aged 14 or something when you start getting to the point where you learn maths you don't really need outside of specific careers (eg trig), whereas every British person had covered basics of fractions before that, even if (in some cases) we'd learnt decimals and percentages first (which we then did later, but still way before 14).

[Brandon]

Fractions also, IMHO, make more sense than tenths, at least around here.  In this area, Chicagoland, we have a system where there are 8 blocks to the mile, thus one block equals 1/8 mile.  1/4 mile is two blocks, 1/2 mile is four blocks.  We also tend to put up the block number of the street on the signage in the City of Chicago, as below:

[jakeroot]

I don't care how great fractions are -- they still belong to an archaic system of measurements that should have been dumped long ago.

[english si]

I don't care how great fractions are -- they still belong to an archaic system of measurements that should have been dumped long ago.

You "don't care how great fractions are" - so this purely spite, rather than reason or utility.

You think fractions belong to the metric system - you are mathematically illiterate.

"archaic" - metric is as old as customary, and is almost the epitome of the long-discredited Modernist Epistimology (that with arbitrary pretensions to universalism we can transcend our culture bound reality into glorious knowledge).

"should have been dumped" - but in every country where the assholes like you didn't get their aim of ideological suppression of non-metric units, customary has hung around (even if, in the UK, it is to a much lesser extent than the US). Plus your reason for dumping them is not about utility (you don't care how great they are), nor a valid argument - ditch them because they are old (even if Metric was newer, which is isn't) isn't a valid reason to ditch them, but rather arrogance.

[J N Winkler]

I don't care how great fractions are -- they still belong to an archaic system of measurements that should have been dumped long ago.

Vulgar fractions are a type of notation for rational numbers and are not inherently part of any measurement system.  Decimals and metric do tend to go together because both are base-10 systems.  It is only because metric units measure physical quantities, which brings significant digits into play, that the main shortcomings of decimals compared to fractions--e.g. the lack of simple notation for infinitely repeating decimals like 0.333333333333... or 0.121212121212121212...--can be ignored.

Where signs are concerned, there are some practical considerations that come into play.

*  As English Si mentions, it is normal in both Britain and the USA for fractions to be part of basic arithmetic education.  Things may have changed a bit since I was in elementary school owing to the introduction of calculators in the classroom, but I remember fractions being introduced no later than third grade and decimals no earlier than fifth grade, with the idea of fractions having powers-of-ten denominators being used to segue into decimal notation.

*  Guide signs are visible long before they can be read properly, so it is valuable to have a convention that allows smaller-than-unit components of a distance expression (whether metric or customary) to be recognized as such long before the actual values can be read.  In the case of decimals this is difficult since the decimal point is indistinct and easy to miss among digits of equal height.  Some countries (and Arizona on I-19) do this by having a convention that near distances (e.g. for an upcoming exit) will be given in meters rather than kilometers.  In the miles-and-tenths era, California did this by using smaller digits for the tenths and underlining them.  Québec and some other jurisdictions use a decimal comma (which in Univers is more readily differentiated from a dot than is the case in Series E Modified) and smaller digits for the less-than-unit component.  But for vulgar fractions the solution falls out of the notation itself:  if you know how to design a fraction rectangle properly for signing purposes (always use a 60° slash) as in the USA, or have available a set of fraction glyphs in your traffic signing typeface (as in Britain), then you are done.

In regard to historical use of fractions on guide signs in the US, the various editions of the MUTCD up to at least 1935 are agnostic.  No sign illustrations are shown with fractional distance expressions but the text itself uses irregular fractions with customary units for post heights and the like.  At the national level, a distance expression in hundreds of feet right on the diamond sign itself was the preferred alternative to a separate distance plate that would now be used with a warning sign.  I suspect the 1961 MUTCD was the first national edition to show guide signs with fractions since it would have included signs from the 1958 AASHO Interstate signing manual for use on non-Interstate freeways with either a black or green background (the black-background option for non-Interstates was later cancelled in 1971 or 1978).

However, there were many state MUTCDs well before 1961 that provided for the use of fractions on signs and diagrammed them.  The 1949 Kansas MUTCD, for example, called for fractions to be used with the old historical-marker sign that had its legend on top of a buffalo silhouette.

In the case of California, I don't think miles and tenths on interchange sequence signs would have seemed as anomalous at the time as they now would in the context of vanilla Interstate signing.  In the 1958 edition of Chapter 8 of the Planning Manual of Instructions, as the Caltrans traffic manual was then called, none of the signing typicals for freeways actually shows an advance guide sign with a distance expression.  The phrases "Right Lane" or "Left Lane" (note initial capitalization) were used instead (though by 1958, downward-pointing arrows were used for left exits, probably to address expectancy issues).  The only standard signs intended for use on freeways that had vulgar fractions were the black-on-yellow "END FREEWAY" series.

[jakeroot]

You think fractions belong to the metric system - you are mathematically illiterate.

As I worded my comment, yes I am mathematically illiterate. But my intent was to say that fractions belong with the imperial system in relation to the roads. In other words, the few countries that use miles per hour for speed limits, so far as I know, use fractions for distances (perhaps some countries use km/h and fractions, though I doubt it). Fractions, yes, do not belong to any system of measurement, but they do tend to get grouped into the imperial system since metrication sort of mandates base-10 measurement, and only 1/2 & 1/5 are base-10 fractions. And from the perspective of a sign engineer, 1/2 and 1/5 aren't really enough for distances less than a natural number.

"archaic" - metric is as old as customary, and is almost the epitome of the long-discredited Modernist Epistimology (that with arbitrary pretensions to universalism we can transcend our culture bound reality into glorious knowledge).

"should have been dumped" - but in every country where the assholes like you didn't get their aim of ideological suppression of non-metric units, customary has hung around (even if, in the UK, it is to a much lesser extent than the US). Plus your reason for dumping them is not about utility (you don't care how great they are), nor a valid argument - ditch them because they are old (even if Metric was newer, which is isn't) isn't a valid reason to ditch them, but rather arrogance.

"Archaic" meaning old but still shit. "Archaic" is not synonymous with just old, but rather old and out-of-date. The metric system is older, yes, but compared to imperial measurements, metric is much more relevant in a progressive society. A measurement system whereby everything has to reference 5280 feet doesn't make a lot of sense to me, especially since 1/4 of a mile is still referencing 5280 feet, just 1/2 of it, of which no one knows. At least 1/2 of a kilometer is 500 meters (the key here is that you can easily reduce the unit to another whole number).

[formulanone]

Fractions also, IMHO, make more sense than tenths, at least around here.  In this area, Chicagoland, we have a system where there are 8 blocks to the mile, thus one block equals 1/8 mile.  1/4 mile is two blocks, 1/2 mile is four blocks.

This is probably the best reason to keep fractions; most interstates/freeways began in urban areas, so it would seem natural to continue to use them as they spread out into the suburbs and rural areas. I think we tend to have a picture in our mind about what a quarter or half is quite readily.

I don't care how great fractions are -- they still belong to an archaic system of measurements that should have been dumped long ago.

Americans tend use fractions, rather than decimal amounts, in everyday talk. Perhaps only when quoting a statistic do we go into the world of decimals...outside of technical, mathematical, or specific uses (say, gun barrel calibers). With statistics, it's later lazily rounded by some authority into a simple fraction for misleading emphasis.

For road measurement, there should be some consistent amounts - such as 2500 or 1250 feet, since they're very close to 1/2 or 1/4 mile - but I think the concept of that distance is a bit trickier to picture. Then again, many Navigation units tend to side with amounts like "in one thousand feet, turn left" or "in 400 feet, turn right" which is terrible (well, to me at least) in places with many side streets comprising city blocks.

Older signs with underlined miles and tenths would have persisted for a considerable length of time since porcelain enamel on steel, which was favored for sign substrates at the time, has a service life of fifty years or more.

Which has me wondering if any sort of smaller examples exist off the mainlines, or on old/former routes...

Vulgar Fractions would be a great name for a band.

Very much this.

[mrsman]

And furthermore in many areas, particularly in the Midwest and West Coast, there are grids of streets based on the mile.  Major streets are a mile apart.  And at the half mile points are minor arterials and at the quarter mile points are collectors.  Other streets are generally local and probably do not intersect major streets at traffic lights and likely are riddled with cul de sacs.  So this reinforces the importance of keeping fractions and not decimals.

Example in the SFV Valley:

Sepulveda (major arterial) 0
Noble Ave (collector) 1/4
Kester Ave (minor arterial) 1/2
Cedros Ave (collector) 3/4
Van Nuys (major arterial) 1
Tyrone Ave (collector) 1 1/4
Hazeltine (minor arterial) 1 1/2
Ranchito (collector) 1 3/4
Woodman (major arterial) 2

[jakeroot]

All things considered, would you guys support a movement towards metric units on our highways? Everything I'm reading above seems to indicate a strong preference for imperial units.

[vtk]

All things considered, would you guys support a movement towards metric units on our highways? Everything I'm reading above seems to indicate a strong preference for imperial units.

People prefer what they're used to. In everyday life, I don't consider the metric system to be superior or inferior to the imperial system, but I prefer imperial because that's what I encounter all the time. (Even when I design large things like interchanges, I prefer measures that are nice fractions of a mile, rather than round numbers of feet, because of the historical use of rods and chains in surveying, and I have memorized those measures expressed in feet.) Converting the United States to metric would be a huge undertaking for almost no practical benefit, and would rightly face massive public resistance.

[briantroutman]

I had a very strong primary and secondary education that covered–in great depth–decimals and fractions, the US customary system of measurements as well as the metric system. So anything that I say is most certainly not founded in ignorance or lack of exposure.

When I first learned about the metric system around age 7 or so, I was immediately 100% gung ho in favor of switching to it and never looking back. What a stupid country we live in, I thought, to be mired in such archaic measurements as feet and inches when the rest of the world has surpassed us with these metric units.

Then, maybe about a decade later, my thinking started to evolve, and I ended up doing almost a complete 180. Yes, in the beautiful metric system, 1 cubic centimeter, if filled with water, contains exactly 1 milliliter, and it takes exactly one calorie to raise that water (which weighs one gram) one degree celsius.

So what?

In a day and age when we calculate most data electronically, the ability to interrelate the various metric units is, as far as I can see, largely irrelevant. Today, if you're designing some kind of physical object, you'll be doing it in a CAD system which will be happy to give you the object's volume in cubic centimeters, pints, dekaliters, and cubic furlongs faster than you can drop a new decimal point on the page.

So as far as I'm concerned, the question then becomes what unit best fits the scale being described. For on-road motor vehicle travel, 0 mph is ridiculously slow (stopped, actually) and 100 mph is ridiculously fast. 0°F is ridiculously cold and 100°F is ridiculously hot. I think it's no coincidence that some metric units that have caught on in the US, like the two-liter bottle of soda or a gram of weed, are often very convenient package sizes.

[english si]

"Archaic" meaning old but still shit. "Archaic" is not synonymous with just old, but rather old and out-of-date.

The metric system was never in-date. It's aim was to transcend 'in-date'.

The metric system is older, yes, but compared to imperial measurements, metric is much more relevant

I really don't see how 100 trillionths of the (incorrectly calculated - and obviously never measured until satellites) distance between the north pole and the equator via Paris has any relevance to anything.

But that was the point of the metric system: to be divorced from real-world considerations and as arbitrary as possible. OK, now a metre is the distance a very specific type of light travels in an almost unmeasurable unit of time, rather than a rod in Paris based off calculations of a meaningless nature, but the point was that the units were meant to be totally irrelevant to anything.

in a progressive society.

</facepalm>

As an aside - the Revolutionary France that created the metric system is one of the best arguments against a 'progressive' society. The wheel of revolution kept turning and turning, leaving destruction and death in its wake as they hunt for progress (and even today, people are risking death to escape France and into a 'backward' country that uses miles on road signs). The metric system wasn't invented to give a nice systematic system, but to burn all bridges with the past, with culture and tasks and to try and transcend into glorious Reason. Metric time measurement died after the Reign of Terror as it was too blatantly incompatible with everyday life - the other stuff is bearable, but similarly designed to try and mould the universe to us, rather than us to the universe.

A measurement system whereby everything has to reference 5280 feet doesn't make a lot of sense to me, especially since 1/4 of a mile is still referencing 5280 feet, just 1/2 of it, of which no one knows.

1/2 a mile is referencing half a mile. And, unlike the 100 trillionths of the distance between north pole and equator on the Paris meridian, the customary system isn't tied to miles, or feet - it's tied to nothing in particular (though obviously has undergone standardisation).

At least 1/2 of a kilometer is 500 meters (the key here is that you can easily reduce the unit to another whole number).

which, actually, is perfectly easy to do with miles, if you use yards. 1/16 of a mile = 110yds :. 1/2 a mile = 880yds. Thirds are difficult in both - fractions are good here! Though, of course, the reason that customary has many different units with odd conversion ratios is that the idea was that for a given task you used one or two distance units and stuck with it. It doesn't matter if you didn't know that there are 80 chains in a mile - unless you are measuring railways! And you'd never need to know that there are 5 chains in a furlong, unless you were converting a rail marshalling yard into a horse racing circuit!

All things considered, would you guys support a movement towards metric units on our highways? Everything I'm reading above seems to indicate a strong preference for imperial units.

I'm open to either, but change for the sake of change or 'progess' is a shitty reason.

In North America the mile is an important tool for navigating highways due to the grid systems, and fractions common - mrsman's good example of knowing how important a road is by whether it has a whole number or a fraction on the sign shows that.

People prefer what they're used to.

Indeed.

In everyday life, I don't consider the metric system to be superior or inferior to the imperial system, but I prefer imperial because that's what I encounter all the time.

True - I'm bilingual when it comes to units as I encounter both quite a bit (though imperial tends to be hidden in metric units - eg 5cmx10cm wood in lengths that are expressed as multiples of 300mm - rather than 2-by-4 in lengths that are in feet).

I've noticed a gradual metrication of the UK - and have given the temperature as the best example before (and do so again, below). But it's been through the genuinely liberal and progressive of gradual change, rather than the coercion and banning that everyone else used to get there.

Converting the United States to metric would be a huge undertaking for almost no practical benefit, and would rightly face massive public resistance.

Indeed. The other hold out - the UK, was less aggressive than it's former Dominions (Canada, Australia) in metrication and caved in to resistance - allowing dual units and stuff like that. Gradually the UK is becoming more metric and imperial measures are fading out, but far from totally and full conversion will never happen (though it's only road signs and draft beer/cider that is officially imperial).

Then, maybe about a decade later, my thinking started to evolve, and I ended up doing almost a complete 180. Yes, in the beautiful metric system, 1 cubic centimeter, if filled with water, contains exactly 1 milliliter, and it takes exactly one calorie to raise that water (which weighs one gram) one degree celsius.

So what?

Oh, it matters to those who like things neat and tidy, but it matters not one jot outside the OCD world. The litre of water weighing a kilo has some use, though the US's fluid measures cover that (better than the UK's) rather well, with a pint weighing a pound rather than needing the mnemonic "a pint of water weighs a pound and a quarter" that the UK's 20oz pint brings. Calories aren't used, except kcal on food packaging (alongside kJ) - and heating up a litre of water 1C is an inconceivable and unrelateable quantum of energy when it comes to "I'm putting this in my body", but then a Joule is also an irrelevant equation - there's no reason why it couldn't be in ergs. They are just numbers that you compare to other numbers. Which brings us on to the ultimate comparison thing - temperature:

0°F is ridiculously cold and 100°F is ridiculously hot.

Fahrenheit was, while weird, designed (later than Celsius) to be perfect for the weather - most of Germany, the UK, etc stayed within that 0-100 scale, so little use for three digit numbers, and even less for the, far more annoying, negative numbers.

And the finer grain of scale gave more accuracy without needing to leave integers behind.

Gradually (and probably in part to a media that thinks a bit like jake that metric is hip and progressive) the UK has moved from Fahrenheit, to a dual system with both F and C with Celsius being given increasing prominence over time in winter but Fahrenheit still ruling summer*, to where Fahrenheit only comes out in summer but still gets a roughly equal footing when it does, to one where Fahrenheit has disappeared outside detailed forecasts and footnotes.

*'Celsiheit' - because '32 degrees' sounds neither hot nor cold, and 0 or 90 is much better!

I think it's no coincidence that some metric units that have caught on in the US, like the two-liter bottle of soda

Though there's little reason why that isn't half-a-gallon. In the UK, supermarket own-brand milk, bought at supermarkets (rather than convenience stores - where they moved to metric to help hide the higher price per ml) are multiples of pints - sold in ml, but with big numbers with no units to get around the law on metric-first. With milk, there's clearly a demand for pints, rather than 500ml multiples, else the supermarkets wouldn't go to the trouble, but it's a strange thing that people care.