Converting everything to standard form (which is a more extreme example) is something I learned when we had slide-rules at school, and I was glad to leave it behind when I got my first scientific calculator.
Admittedly, it does require a working knowledge of all the prefixes.

And that's the kicker -- either approach requires that working knowledge of all the prefixes (or at least the relevant ones -- I certainly can't claim a working knowledge of yotta and such).

In the slide rule (and trig/log table) days, people developed that engrained working knowledge as a survival mechanism. As with so many things, we are victims of our own technological success. The tools available to us not only enhance our productivity enormously, but that make it not only possible, but largely inevitable, that a large fraction of people that, yesteryear, would have had a strong command of these skills, today are incredibly deficient. I've stopped being surprised at the number of graduate students in computer science that cannot figure out what 63 divided by 7 is without a calculator.

 

And that's the kicker -- either approach requires that working knowledge of all the prefixes (or at least the relevant ones -- I certainly can't claim a working knowledge of yotta and such).

In the slide rule (and trig/log table) days, people developed that engrained working knowledge as a survival mechanism. As with so many things, we are victims of our own technological success. The tools available to us not only enhance our productivity enormously, but that make it not only possible, but largely inevitable, that a large fraction of people that, yesteryear, would have had a strong command of these skills, today are incredibly deficient. I've stopped being surprised at the number of graduate students in computer science that cannot figure out what 63 divided by 7 is without a calculator.

After a few years in the industry one develops an ability to look at an oscillator/filter/delay and know immediately what sort of capacitor/resistor values it will need whether it is a tiny ceramic, a box-poly or a huge electrolytic, and if the calculated answer doesn’t agree then to calculate it again.
I’ve never needed prefixes more than Giga (load resistor for a condenser mic) of femto (current noise of a decent JFET op-amp). Anything beyond that is just for journalists trying to look impressive, and avoid measuring things in weight-of-elephant/area-of-football-pitch/size-of-double-decker-bus/size-of-Wales (or whatever they use in your country).

 

I've stopped being surprised at the number of graduate students in computer science that cannot figure out what 63 divided by 7 is without a calculator.

Very sad. We had to memorize the multiplication table to 12x12 in the 4th grade.

 

Very sad. We had to memorize the multiplication table to 12x12 in the 4th grade.

Nope. We had to memorize up to x16 table.

 

I had students who needed a calculator to determine 8-bit ADC step size with 2.56V reference.

 

Very sad. We had to memorize the multiplication table to 12x12 in the 4th grade.

Same here, though I never really understood the rational for going beyond 10x10, since that's all that's needed as a foundation for doing base-10 arithmetic. That's not to say that the additional entries aren't useful, but the same could be said for multiples of higher values, too. So why not got to 15x15 or 20x20? Given our field, we can certainly see a value for up through 16x16, but that's not enough of a reason to require it of all kids.

 

I had students who needed a calculator to determine 8-bit ADC step size with 2.56V reference.

It still manages to amaze me how many comp sci majors don't know what 2^8 is. Or how many bits are in a byte (nowadays).

 

Same here, though I never really understood the rational for going beyond 10x10, since that's all that's needed as a foundation for doing base-10 arithmetic.

Since I didn't memorize beyond 12, I just do mental arithmetic for anything above 12.

My 4th grade teacher also taught us other number bases (2, 3, and 4 as I recall), but she used nonsensical names (I think to avoid confusing us). She called one pollywog. It really solidified the concept of carrying and borrowing.

 

Actually, The Art of Electronics 3rd Edition was released for PDF distribution and can be found <snip> on the Internet Archive. Which is very scrupulous about not having any book currently in print available without the author's consent. Don't know why Paul released it but he apparently did.

 

Since I didn't memorize beyond 12, I just do mental arithmetic for anything above 12.

My 4th grade teacher also taught us other number bases (2, 3, and 4 as I recall), but she used nonsensical names (I think to avoid confusing us). She called one pollywog. It really solidified the concept of carrying and borrowing.

I don't recall when I was introduced to other number bases. Sometime in junior high. I don't recall us doing anything beyond base-12, using T for ten and E for eleven as the symbols. I recall thinking that that would make doing base-13 hard, because you would need two T symbols. I don't think it occurred to be, then, that a symbol is just a symbol and you can use whatever you want. But perhaps that is why the curriculum had up through 12x12 -- because it was seen as useful background when number bases were covered later.

 

Actually, The Art of Electronics 3rd Edition was released for PDF distribution and can be found <snip> on the Internet Archive. Which is very scrupulous about not having any book currently in print available without the author's consent. Don't know why Paul released it but he apparently did.

How do you/we know that it was authorized by him? I didn't see anything obvious, just that is was uploaded by some user named Prakhar_Mishra1.

 

It is AAC's policy not to post links to copyrighted material. All links to AOE have been deleted.

 

Actually, The Art of Electronics 3rd Edition was released for PDF distribution and can be found <snip> on the Internet Archive. Which is very scrupulous about not having any book currently in print available without the author's consent. Don't know why Paul released it but he apparently did.

I thought the same thing, but since it seemed odd, I researched it and found this on the AoE website:

​

It turns out the Internet Archive is not as on-board with author’s rights as it may appear. Their “lending library” no matter how well meaning, and its moral standing is a matter for debate, uses pretty slimy tactics to “own a copy” of everything they lend. It looks less pretty the more you dig.

I would say the AoE website is pretty authoritative. Only Kindle is legitimate, it seems.

 

I didn't see the e-book note but I did notice the counterfeit notice. I do seem to remember some online discussion quite a while back that Paul was allowing PDF versions to be distributed but it must have been in error. Mea Culpa...

 

I didn't see the e-book note but I did notice the counterfeit notice. I do seem to remember some online discussion quite a while back that Paul was allowing PDF versions to be distributed but it must have been in error. Mea Culpa...

I had a similar idea—Internet Archive, and such a clean PDF—but something wasn't right, so I went looking. In fact, it was because I was going to post the link here and wanted to be sure it was legit. I would have posted a warning about it, but that seemed like it would cause as much trouble as posting the link since most people don't seem to care about the copyright infringement.*

*to be completely clear, I am not numbering you, @SamR, among them

There are real questions about the what is "right" in these cases, but when the authors have the legal right to decide what happens to their work, I can't see the potential downloaders as victims, which would be the reason I might seek to circumvent the author's attempts to protect the work. But, this is just not the kind of case we are dealing with. The only ones that can legitimately claim harm are the owners of the work.

I've made some of my income from writing books in the past. I know that my livelihood was directly tied to the number of copies sold. PDFs and e-books didn't exist at the time. Counterfeit books on the other hand did. This was an unlikely fate for my books, which sold well but couldn't have repaid the investment of bootlegging them. Large scale plagiarism, though, was a real threat in that it took my work and used it to compete for the sales of the books I made money from.

So maybe I am a little more sympathetic to the authors, but when you know how much work writing a book like that is, and how much time and effort are exerted, it's hard not to choose to respect whatever distribution scheme they choose.

 

As with so many things, we are victims of our own technological success

Back in the day of corded phones with handsets connected via a curly cable I used to know at least a dozen phone numbers. Today I hardly remember my own number. Little better with the wife's number - but - - - . Today if my cell phone goes dead I'm lost. But then again you can't even find a pay phone.

We had to memorize up to x16 table.

YIKES!

I never really understood the rational for going beyond 10x10, since that's all that's needed as a foundation for doing base-10 arithmetic.

Long ago I developed a way of thinking of higher number multiplication. For example:
17 x 8 = 17 x 10 - 17 x 2
17 x 2 = 34 (lock that number away in memory - 34!)
17 x 10 = 170 (easy)
170 - 34 = 136. All done without a calculator.
170 x 8 = 136 (done with a calculator) (faster and more certain of being right but what if you don't have a calc' available?)

The title of the thread is "Teaching an old dog new tricks." So this is not off topic, this is just another trick, one this old bird still uses from time to time. Works with even higher numbers. Round to the TEN's then add or subtract the odd little part.
17 x 12 = 17 x 10 + 17 x 2 = 204
For those lacking in "Order of Operations" - Parentheses ( ) first. Powers and Roots second. Multiplications and divisions third. Finally add and subtract.
17 x 10 = 170
17 x 2 = 34
170 + 34 = 204

MY trick to numbers. And numbers have always been one of my weaknesses. Graduated from the #4 worst school in the LAUSD (Los Angeles Unified School District) with poor basic math skills. What little I know of Algebra I had to figure out on my own. And there's a LOT of it I still don't know. Nor, at this point in my life, do I care. Tape measures and fractions are the things I use the most.

 

LOL I remember years ago being in a mall in Birmingham Alabama and made a purchase for $3.86 with no tax. Gave the girl a $5 dollar bill and she said her cash register wasn't working. I told her no problem, give me $1.14 in change. She got all flustered and finally found a calculator and did the math then looked at me with wide eyes and said "How did you do that?" I just smiled and thought to myself "because I finished 3rd grade"...

 

I remember years ago being in a mall in Birmingham Alabama and made a purchase for $3.86 with no tax. Gave the girl a $5 dollar bill and she said her cash register wasn't working.

I'd've given her $5.11 so I'd get fewer coins back.

I've lost count of the number of times that a cashier told me that I gave them too much money. Then I explain why I did it and they'd enter the amount I gave them so the register could calculate change for them.

I wonder if it ever occurs to them that their statement is obvious. If they have to give me *any* change, I gave them too much money...

 

I'd've given her $5.11 so I'd get fewer coins back.

I've lost count of the number of times that a cashier told me that I gave them too much money. Then I explain why I did it and they'd enter the amount I gave them so the register could calculate change for them.

I wonder if it ever occurs to them that their statement is obvious. If they have to give me *any* change, I gave them too much money...

I used to do that but stopped. It's not worth the hassle to confuse the poor cashier. One time, the cashier call the supervisor for help and he gave me back my coins saying "we can't do that".

 

I used to do that but stopped. It's not worth the hassle to confuse the poor cashier. One time, the cashier call the supervisor for help and he gave me back my coins saying "we can't do that".

Lots of similar experiences. At Arby's a couple of years ago the order came to something like $4.87 and I gave them a $5 and while I was fishing in my pocket they rang in the $5 and I handed them $0.12 just as the drawer opened. They were completely lost on what to do and had to call a manager, who told them that they had to void out the order and start over. While they were doing that, the manage chastised me for not telling the clerk that I was going to give them additional change. I was thinking, well, if Arby's hired managers and cashiers that could add 13 and 12, that might solve the problem, too.

I had another time that the bill came to $5.01 and I gave them $10 and a penny. They had no idea what to do.

Then, of course, there's the time that I convinced a 16 year-old girl that she was only fourteen because her math skills were so bad (and because she believed whatever number a calculator spit out at her).