When I was in college and calculators were first beginning to replace slide rules, one of my math professors said, "A calculator will give you the wrong answer to 15 decimal places."

After a few years of trying to teach electronics students back-of-the-envelope calculations of electronics problems, to little avail....I began confiscating calculators on the first day of class...only allowing them AFTER they'd demonstrated they could perform simple calculations.

In addition, I emphasize the point that unless you're building instrumentation, resistor, capacitor, and inductor values are only to 2 significant figures....even the 5 percent ones. It makes NO sense to work out calculations to 5 decimal places, when no components are accurate to more than 2.

When a student asks...."Should we use 3.14159 or 3.1416 for PI?" I answer....How about 3??!! That's as close as you'll need to pass ANY FCC exam....as well as create a functioning circuit.

We need to start teaching students again some general "feel" type of problems before we try plucking eyebrows on a termite. An electronics student should be able to look at a coil and tell if it's 1 henry or 1 microhenry.

Stay tuned

 

Agreed, and same notion applies to areas other than electronics. If you don't understand the problem, significant figures don't matter. The classic rope around the Earth problem is just one example.

John

 

My work usually involves 5 or more decimal places. When you get into precision digital instrumentation, π=3 doesn't cut it.

 

The only 2 significant figures in my life were my wives.

But seriously, I do 1% analog designs. 3 digits are almost enough.

 

In some cases, 3e18 and 6e18 is essentially the same number. Zero doesn't exist sometimes.

 

Since back of the napkin calculations may now be done in a spreadsheet, I found value in keeping precision until the end. For instance it gives a way to check if two alternative ways to calculate the same thing actually do give the identical result. No worries about potential rounding errors causing an apparent discrepancy.

I also used precise values for constants because I could look at the work years later and know if it was mine. A 3.14 was a sure sign it wasn't my work.

 

Good point. Two many people think that π = 22/7.

A better value would be 355/113 which is good to six decimal places.

In programming, one can use 4 x atan(1) or acos(-1) for pi.

 

In programming, one can use 4 x atan(1) or acos(-1) for pi.

Ah, but then your trust (known mathematical relationship) in the result is actually faith (unknown internal calculation) in the compiler... And in the processor executing the code. Pentium, anyone?

For the young'uns out there:
https://en.wikipedia.org/wiki/Pentium_FDIV_bug

ak

 

For Pi, I use
1000000 * Pi = 2^20 * 3.

Then I work in integers. Above gives 0.1% accuracy.

EDIT: and now I realize @MrChips replied to a 9-month old thread.

 

EDIT: and now I realize @MrChips replied to a 9-month old thread.

What a lightweight! I've responded to posts WAAAAAY older than that.

ak

 

The only 2 significant figures in my life were my wives.

Hola No. 12,

Pity it does not translate easily into Spanish; otherwise I could steal that line for my unauthorized list.

 

Good point. Two many people think that π = 22/7.

A better value would be 355/113 which is good to six decimal places.

In programming, one can use 4 x atan(1) or acos(-1) for pi.

Hi,

The idea is to try to find an approximation that gives more digits than you put into it. I dont know if there is one for pi but there are interesting ones like that.

Another interesting one is this:
pi/2=38*1373/(35*13*73)

where the more interesting part is that the top has 1373 in it and the bottom has 13*73 in it. If we cheat a little and call the 1 and 3 and 7 and 3 repeated in the denominator, that means we required 3,8,1,3,7,3,3,5 which is 8 digits for at least 10 digits of precision.
3.14159265358979 [more exact]
3.14159265392142 [approx]
3.14285714285714 [22/7] (3 digits from 2 digits, or from 3 digits)