Ask HN: real world examples of numbers with 3 decimal places | Hacker News Reader

Ask HN: real world examples of numbers with 3 decimal places

19 pointsu29626 comments

sorry this is off-topic but there seem to be a lot of mathematicians here. I'm an elementary teacher and currently teaching children about decimal places and place value. I try to use real world examples to teach maths whenever possible but I can't think of any using 3 decimal places that would be relevant to such young children (aged 8-9).

any ideas?

View on HN

I'm an elementary teacher

Definitely baseball statistics for that audience. Also finishing times for sprints to thousandths of a second.

Not to answer your question, but to suggest useful resources for elementary math teaching, I'll suggest

http://www.amazon.com/Knowing-Teaching-Elementary-Mathematic...

an essential book for someone in your profession, and

http://www.amazon.com/Vision-Elementary-Mathematics-W-Sawyer...

a book with wonderful teaching tips, and

http://www.amazon.com/Elementary-Mathematics-for-Teachers/dp...

a very excellent set of exercises for any elementary mathematics teacher preparing lessons, and a great guide to the best available series of mathematics textbooks in English.

You might also try asking your question on the appropriate forum

http://www.artofproblemsolving.com/Forum/index.php?f=300

(the forum is really for middle school math, but you could give it a try) on the Art of Problem Solving site, a generally good site for discussion of math.

How about measuring distance using the metric system. How tall are you? How long is your hair? (in metres) How big is this room? How far is it to your house?

They should be able to convert from being 127 cm tall to being 1.27 metres tall, and then be able to run around measuring things that are a fraction of a metre and multiple metres.

A good concept to add would be understanding things in multiples of ten. For instance, once they know it is 1.5 kilometres (1500 m) from their house to the school, they can use their understanding of decimals to tell them it would take roughly 1000 kids like them laid end-to-end on the sidewalk to cover the distance from their house to their school. ... They know this just from shifting the decimal point when comparing 1500 m to 1.27 m. If you are lucky, they will even think about this lesson on their walk home!

(roughly 1000 is a better estimate than 100 or 10,000 and in many situations, that kind of estimate is good enough)

Getting the order of magnitude right is actually a problem for some folks. I remember a pilot in Eve thinking that his 10,000 km/s speed in real-space could actually make a significant dent in distances measured in parsecs. (Not in under a minute!)

The problem with using the metric system in the US is that it really isn't applicable to most real life situations and feels quite artificial. I recall having that feeling as a child while being taught the metric system.

It's funny that they show you the superb benefits of the metric system very early and when it is most apparant while doing basic arithmetic, yet you live in a country where regular use of the metric just can't happen.

> it really isn't applicable to most real life situations

the irony is that as 1 liter of water weighs 1 kilogram estimates of various things is made much easier.

I've often used that relation to my benefit.

I don't disagree that the metric system is simpler, but that's maybe not the best example, because the U.S. system has a similarly simple water volume-weight equivalence, and it even has a catchy saying: "A pint's a pound, the world around". :-)

Medicine: the pH of an arterial blood gas (ABG) sample is typically given out to 4 digits. 7.380 is about normal. 7.211 might seem about the same as 7.219, but if one sample is 7.211 and 15 minutes later it's 7.219, you're doing something right. If it's 7.219 and in 15 minutes it goes down to 7.211, something is very wrong.

Machine shops and engineering: every machinist makes every cut to, at a minimum, the nearest thousandth of an inch, and often to the tenths of thousandths; often over several inches (like piston heads and cylinders) This is what slip-clutch micrometers are for.

A red optical filter for a physics experiment could easily be accurate to 720 nanometers with a band pass of 719.998 to 720.003 +/- 2 in the next digit. There are lots of examples in physics, go get a physics supply catalog.

Awesome examples, but I would imagine that none of them would apply to someone in elementary school (K-5, or children 10 and under, basically).

Trauma medicine, race car engines, and lasers. What kid under 10 wouldn't be totally into those?

stock prices gas prices(granted they use 9/10 as a fraction, but it can be stretched)

p.s. you'll be happy to know that if you search google for "real world numbers with 3 decimals" this thread is the #1 result

baseball batting averages.

for that matter, slugging percentage, on base percentage etc etc. many baseball stats use 3 decimal places. baseball drew me into statistics when i was that age.

Don't use slugging percentage - it's not a percentage at all. Singles are 1, doubles are 2, triples are 3, and home runs are 4. It's a terribly named statistic that's on its own bizarre scale.

Wow. Thanks to Wikipedia, I've finally understood the mysterious slugging percentage. Sorry, not a huge baseball fan.

true, BUT... 3 digits are generally the norm and he original poster didn't specifically mention that he wanted percentages. i would say slugging percentage is another good example because you can go into the ideas of how it is actually determined. the arbitrariness of it. leads into lots of other wonderful esoteric basbeball stats, vorp and all the rest.

1/8 = one slice of pizza

1/8 = one slice of pizza

How does this even answer the question that was asked?

(It's hardly likely that an elementary teacher would need this suggestion, as all elementary math textbooks show fractions as slices of pies or pizzas.)

Do you mean because one-eight of a whole is 0.125 of a whole? That would be a good reason to teach the decimal representation of that fraction, if that is what you are suggesting.

P.S. Some pizza restaurants I frequent here cut pizzas into twelfths. This probably depends on local custom and the size of the pizza.

The question that was asked was: Any ideas?

That was my idea - a real-world example (for the age group) of why the third decimal place is important.

Regarding your local pizzas, it was an example - it may not be valid for all situations, unfortunately, but there's no dependency.

I'm surprised you didn't write 1/8 = 0.125 to make the point clear, because 1/8 of ANYTHING is 0.125 of the whole thing.

A cut of pizza into eighths can be done visually (and probably usually is done visually) with no knowledge of decimals at all.

Fractions of time would probably be full of fail, since it uses a different scale since it's time.

Try to think of an example using video games, maybe some RPGs use three decimal places somewhere for stats.

Somehow as a civilization we must have decided somewhere that 2 fixed floating point places was plenty for 99% of things, because you usually never see any more than that unless you get into science.

Another possible way would be to show percentages, but that might also complicate things if they don't know about them yet.

Not sure if this is how it works in the US but our petrol prices are often technically 3 decimal places. 1.059 etc.

Interest rates (such as for mortgages) are often in three decimals e.g. 4.875%

Sales Tax in my city is 6.5% so as a decimal it hits the mark.

Lap times in F1/NASCAR?

temperature averages?

RDA's and food labelling

http://en.wikipedia.org/wiki/Reference_Daily_Intake

Then you can hide the fact they are doing math while teaching them about healthy eating.

Incorporate things like http://www.sugarstacks.com/ and http://www.wisegeek.com/what-does-200-calories-look-like.htm and you can have some interesting projects going

Reply on news.ycombinator.com