# An easily learned algorithm that generates names for all powers of ten.

https://en.wikipedia.org/wiki/Names_of_large_numbers shows that there are not enough names for large numbers, let alone easy names.

Consider 5.672 * 10¹⁰³. This could be pronounced ‘five point six seven three times ten to the power one hundred three’. Fifteen syllables there.

What if you wanted to pronounce it in the normal way?

You could start by rewriting it as 56 * 10¹⁰² + 720 * 10⁹⁹ . The point of this is that 102 and 99 and multiples of three, unlike 103.

One thousand is 10³, one million is 10⁶, one billion is 10⁹, one trillion is 10¹², one quadrillion is 10¹⁵, and so on, forever. See how the exponent is always a multiple of three?

So we could say ‘fifty-six times ten to the power one hundred two plus seven hundred twenty times ten to the power ninety-nine’. Twenty-five syllables. Or to sound more like a normal number: ‘fifty-six ten-to-the-power-one-hundred-two seven hundred twenty ten-to-the-power-ninety-nine’. Twenty-six syllables.

Let’s shorten it by using ‘ee’ to mean ‘times ten to the power of’ and using ‘one oh two’ to mean ‘one hundred two’ and using ‘nine nine’ to mean ‘ninety-nine’. Then we have ‘fifty-six ee-one-oh-two seven hundred twenty ee-nine-nine’. Sixteen syllables, which is just one more than first pronunciation.

We can shorten it further by replacing ‘ee-one-oh-two’ with ‘tasan’, and ee-nine-nine with ‘pap’ using an easily memorized algorithm that allows you to deduce the name of any power of the ten. I’ll explain the algorithm a bit later in this article. That gives us ‘fifty-six tasan seven hundred twenty pap’. Just twelve syllables. Three syllables fewer than the first, standard pronunciation. And in plain English, too, except for somewhat unfamiliar large power of a thousand and it’s new name that the algorithm generated.

Another possibility is ‘ fifty-six point seven two tasan’. Just nine syllables. Just over half as many as in the first pronunciation.

What else could we do? Because the following is true:

5.672 * 10¹⁰³ = 5 * 10¹⁰³ + 6 * 10¹⁰² + 7 * 10¹⁰¹ + 2 * 10¹⁰⁰

we can pronounce our number yet another way, which is ‘five times ten to the power one hundred three plus six times ten to the power one hundred two plus seven times ten to the power one hundred one plus two times ten to the power one hundred’.

Replacing ‘times ten to the power’ with ‘ee’, and ‘one hundred one’ with ‘one oh one’ and so on, yields ‘five ee one oh three six ee one oh two seven ee one oh one two ee one oh oh’. Instead of ‘one oh oh’, optionally you can have ‘one double oh’, or ‘one double zero’, or ‘one zero zero’.

To make it still shorter, and sound more like a normal number, albeit huge, we can use our name generator again, which yields ‘ five tasam six tasan seven tasat two tasas’. Thirteen syllables. To understand how the system is used with other bases, this is the variation to understand thoroughly.

## How the name generating algorithm works.

Here is the full set of rules for mapping the consonants to the ten numerals:

0 = s, 1 = t, 2 = n, 3 = m, 4 = r, 5 = l, 6 = sh, 7 = k, 8 = f, 9 = p.

(The choice of specific mappings is due my modifying in a consistent way a well-known set of mappings used in memorizing numbers using something called the Major System of mnemonics https://en.wikipedia.org/wiki/Mnemonic_major_system )

Thus 10¹⁰³ is tasam, because only the consonants indicate the numerals of the exponent of the power of ten. 1=t, 0=s, and 3=m, with the ‘a’s as padding in effect. There’s a little more to the ‘a’s but we can ignore that for now.

Note that ‘ta’ is the second name in the list but is ten raised to the first power, so it is probably not a good idea to call ‘sa’ the first power of the ten.

Thus, since ‘a’ means ‘ten to the power of’ and ‘p’ means ‘9’ (the base ten numeral) ‘pa’ means 10⁹. Likewise ‘pap’ means 10⁹⁹. And ‘papap’ means 10⁹⁹⁹.

Every power of ten is specified. You just add the letter ‘a’ as many times as is needed as padding to generate words that are pronounceable and mean ‘two to the power of (something)’ while the superscript part of the power (the something) is specified by the permutation of the consonants. Ten to the power one hundred one (10¹⁰¹) is ‘tasat’, pronounced ‘tassat’. Ten to the power two hundred fifty-three (10²⁵³) is ‘nalam’, pronounced ‘nallam’.

An infinite number of pronounceable names of powers of ten (every power of ten is named) are specified by my system, with most of them being rather long. Are an infinite number of them infinitely long? It depends on whether there are an infinite number of powers of ten whose exponents are integers with infinitely many digits, I think.

The system is optimized for easy recall, or deduction if recall is not possible, of the name of any power of two when the number is thought of and vice versa.

## Teaching the name generating algorithm.

Once the students know the ten names of the powers of ten from 10⁰ to 10⁹ ( which are sa, ta, na, ma, ra, la, sha, ka, fa, and pa) the rules for the mapping of each of the ten numerals to each of the consonants and vice versa can be deduced from those ten names.

So perhaps instead of teaching the rules, one could teach the first ten names of powers of ten. If you want to make that into a single chunk of knowledge, ‘sa, ta, na,… ma, ra, la,… sha, ka, fa,… pa’ trips off the tongue nicely and helps remind students where the commas are in the base ten number as you read from right to left. Or how about ‘sa, ta, na, comma, ma, ra, la, comma, sha, ka, fa, comma, pa’?

And/or why not teach the students to pronounce 9,876,543,210 using only the new names? It is pronounced ‘nine pa eight fa seven ka six sha five la four ra three ma two na one ta’. Or ‘nine pa comma eight fa seven ka six sha comma five la four ra three ma comma two na one ta’. One is sa which is ten to the power zero (10⁰) and is missed. It can be learned separately. Or maybe you could tack on the end ‘zero sa’?

## Tweaking the naming algorithm.

If the names aren’t distinct enough, you could tweak the algorithm to generate other names, yielding ‘five tasama six tasana seven tasata two tasasa’. If even the latter is not clear enough, you could tweak the algorithm in other ways to make the names more distinct but longer, yielding, say, ‘five tatsasmam six tatsasnan seven tatsastat two tatsassas’ or ‘five tadsazmam six tadsaznan seven tadsaztad two tadsazsaz’. I want to use only one vowel because the vowel or vowels can indicate some other stuff, like which base the number is in and/or whether it is a positive or a negative number.

## More from Matthew Christopher Bartsh

My favorite activity is learning new things.