Converse Numbers

Literal Numbers

Although AutoMathic allows certain classes of numbers to be written-out as English words, numbers will usually be entered as a sequence of digits. There are a few restrictions when supplying literal numbers to AutoMathic:

Numbers may contain commas (,) as group separators	1,000,000
Decimal fractions between -1 and 1 MUST have a leading zero	0.396 -0.125
Numbers may NOT be entered using scientific notation of any kind!	1x10^5 3.215e-9

Written Numbers

Usually, numbers will be entered as a sequence of digits, but sometimes the context or style of input would make it more natural to use the written form of numbers. AutoMathic allows using words for simple numbers in the following categories:

Small integers and their plurals	zero, one, two, ..., nineteen ones, twos, ..., nineteens 1's, 2's, ..., 19's 1s, 2s, ..., 19s
Small multiples of 10 and their plurals	ten, twenty, thirty, forty, ..., ninety, hundred tens, twenties, ..., nineties, hundreds 10's, 20's, ..., 90's, 100's 10s, 20s, ..., 90s, 100s
Common powers of 1,000 and their plurals	thousand, million, billion, trillion, quadrillion thousands, millions, ..., quadrillions 1,000's, 1,000,000's, ..., 1,000,000,000,000's (group separator commas are optional) 1,000s, 1,000,000s, ..., 1,000,000,000,000s (group separator commas are optional)
Inverse small integers and their plurals	half, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth, sixteenth, seventeenth, eighteenth, nineteenth halves, thirds, fourths, fifths, ... 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th, 16th, 17th, 18th, 19th 3rds, 4ths, 5ths, 6ths, ...
Inverse multiples of 10 and their plurals	tenth, twentieth, thirtieth, fortieth, fiftieth, sixtieth, seventieth, eightieth, ninetieth, hundredth tenths, twentieths, thirtieths, fortieths, ... 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th, 100th 10ths, 20ths, 30ths, 40ths, ...
Inverse powers of 1,000 and their plurals	thousandth, millionth, billionth, trillionth, quadrillionth thousandths, millionths, ..., quadrillionths 1,000th, 1,000,000th, 1,000,000,000th (group separator commas are optional) 1,000ths, 1,000,000ths, 1,000,000,000ths (group separator commas are optional)
Special numbers and their plurals	negative, nil, nothing, neutral, whole, positive, pair, couple, dozen, baker's dozen, gross wholes, pairs, dozens, etc.
Mathematical Constants	Golden Ratio, e, Pi, Tau, Avogadro's number

Written numbers can always be combined as long as the combination is purely multiplicative, not additive. Also note that the numeric versions of "fraction words" (e.g. "3rds", "10ths", "16ths", etc.) are understood and translated as expected, whether or not they appear after a "/", supporting natural-looking input styles for fractions. For example:

three hundred	3 x 100
forty billion	40 x 1,000,000,000
five sixteenths	5 x 1/16
5 16ths	5 x 1/16
5/16ths	5 x 1/16
two dozen	2 x 12
six gross	6 x 144
half a million	1/2 x 1,000,000

Note that, contrary to standard writing conventions, AutoMathic's combined numbers must NOT be hyphenated (e.g. "two-thirds")... Hyphens would be misinterpreted as subtraction!

Additive combinations are only safe to use when they are not part of a larger term:

three and a half	3 + 1/2
two and five sixteenths	2 + 5/16
2 & 5 16ths	2 + 5/16

Complicated written numbers (that imply multiplication and addition) are usually NOT understood by AutoMathic! Here are ways of writing out 256 that get misinterpreted:

Input	Interpretation
two hundred fifty six	2 x 100 x 50 x 6 = 60000
two hundred and fifty six	2 x 100 + 50 x 6 = 500

The only way to use an additive combination as part of a larger term is to enclose the combination within parentheses to help guide the translation and remove the ambiguity:

Input	Interpretation
three and a half thousand	3 + 1/2 * 1000 = 503
(three and a half) thousand	(3 + 1/2) * 1000 = 3500

Using parentheses works, but it is so unnatural and exacting that it defeats the purpose of using written numbers in the first place! It is most effective to use written numbers for the simple cases and multiplicative combinations only.