Long scale is better than short scale

Hi!

It's been a bit since I've posted anything quite as substantial, so here we go!

I was brought up with what we were led to believe was the "British/French" system of numbers, known as "long scale", which many countries still use, as opposed to the "American/German" version, which apparently Britain now uses, also known as "short scale".

The difference? The powers of ten:

10^n	1000^n	Short scale	Million^n	Long scale, -ard	Long scale, thousand
3	1	Thousand	0.5	Thousand	Thousand
6	2	Million	1	Million	Million
9	3	Billion	1.5	Milliard	Thousand million
12	4	Trillion	2	Billion	Billion
15	5	Quadrillion	2.5	Billiard	Thousand billion
18	6	Quintillion	3	Trillion	Trillion
21	7	Sextillion	3.5	Trilliard	Thousand trillion
24	8	Septillion	4	Quadrillion	Quadrillion
27	9	Octillion	4.5	Quadrilliard	Thousand quadrillion
30	10	Nonillion	5	Quintillion	Quintillion
33	11	Decillion	5.5	Quintilliard	Thousand quintillion
36	12	Undecillion	6	Sextillion	Sextillion
39	13	Dodecillion	6.5	Sextilliard	Thousand sextillion
42	14	Tredecillion	7	Septillion	Septillion
45	15	Quattuordecillion	7.5	Septilliard	Thousand septillion
48	16	Quindecillion	8	Octillion	Octillion
51	17	Sexdecillion	8.5	Octilliard	Thousand octillion
54	18	Septendecillion	9	Nonillion	Nonillion
57	19	Octodecillion	9.5	Nonilliard	Thousand nonillion
60	20	Novemdecillion	10	Decillion	Decillion

...etc.

The details of this table is probably my best backup as to why I prefer long scale to short scale.

As you can see, the long scale directly comes from the Latin of the power of a million, but short scale comes from what seems to be a hack: "a thousand times the power of a thousand"? "One less than the power of a thousand"?

If you're intent on using a thousands-based system, I have suggested a "power of a thousand" name below,with the added benefit that it divides directly into the long scale without having to add such a "hack factor"!

10^n	1000^n	Silly name
3	1	Thousand
6	2	Bisand
9	3	Trisand
12	4	Quadsand
15	5	Quintsand
18	6	Sexsand
21	7	Septsand
24	8	Octsand
27	9	Nonsand
30	10	Decsand
33	11	Undecsand
36	12	Dodecsand
39	13	Tredecsand
42	14	Quattuordecsand
45	15	Quindecsand
48	16	Sexdecsand
51	17	Sepdecsand
54	18	Octdecsand
57	19	Nondecsand
60	20	Viginsand

This is obviously very tongue-in-cheek, but it's one of the times that a common usage of numbers (which I like very much) has disappointed me.

Till next time.

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Algebra is not hard

Permalink | Author: Dan Dart | Published: 2018-07-10 11:30:00 UTC | Tags: algebra apples arithmetic counting difficulty fruit letters manipulation mathematics maths numbers oranges shorthand variable

If I were to tell you that I was taking two apples and three oranges home, you'd know what I mean.

Algebra's the same.

You'd know that if I told you that my friend Geoff (I don't have a friend called Geoff) came home with three more apples and five more oranges, that we would have a fruit party, because we're pathetically hungry.

Using algebra is just the same as having shorthand. Maybe it's not the concept, but it's the shorthand that bothers some people?

I don't know that if algebra is difficult for one person then arithmetic is also difficult, but do let me know if it is this way for you!

All algebra's doing is giving things shorter names so that they can be manipulated more quickly. Perhaps that's where the issues start?

If this therefore confuses you, it may be something deeper.

I'm going to have the letter "r" short for oranges here, as having "o" is too much like zero:

2a + 3r + 3a + 5r = ?

Is it easier if I write it in words?

Two apples, and three oranges, and three more apples and five more oranges, is how many of both?

In real life you'd know to count apples together and oranges together, and even if you do it one by one, I'm struggling to see where the difficulty is in that.

Is the difficulty having symbolic metaphors? (I have to use 🔶 for oranges because Blogger doesn't know about them).

2🍏 + 3🔶 + 3🍏 + 5🔶 = ?

Would one have to count them out to make more sense?

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = ?

That's now just simple rearrangement. Is that somehow easier? So, I move some around and...

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = 🍏🍏🍏🍏🍏🔶🔶🔶🔶🔶🔶🔶🔶

Ta-da!

(I wonder how much all of that costs...)

So I really struggle to understand which bit of algebra is difficult for people. Any thoughts, anyone?

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Unknown (URL) said on 2019-03-09T18:47:48.136Z:

Fair enough, Daniil. I was only referring to the substitution and basic algebra that people learn in school the first time they do it. Of course there are harder parts, but I only meant the actual understanding was a letter meant a number that can be indefinite. But fair point nonetheless.

Daniil Baturin (URL) said on 2018-08-23T19:04:35.154Z:

I'm not sure if anyone is having a problem with this part. I can see how manipulating polynomials, especially the long division, can feel highly unusual to people.

Besides, algebra _is_ hard. ;) The fundamental theorem of algebra remains magical for people until much later, when they learn complex analysis, and they have to just believe it. Proving whether a number is algebraic is still a black art.

Long scale is better than short scale

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Algebra is not hard

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