This library is built in the open.
If you spot an error, have a suggestion, or just want to say hello — we’d love to hear from you.

One, ten, hundred, thousand, ten-thousand, hundred-thousand, million, and ten-million are the names in order. || 2 ||
Then come hundred-million, billion, ten-billion, hundred-billion, trillion, and ten-trillion.
Then the "ocean," the "last," the "middle," and the "beyond-half." These names for the places of numbers, each ten times greater than the last, were created by the ancients for the purpose of practical calculation. || 3 ||
Prose Order: The names—unit, ten, hundred, thousand, ten-thousand original: "ayuta", hundred-thousand original: "laksha", million original: "prayuta", and ten-million original: "koti"; then hundred-million original: "arbuda", billion original: "abja", ten-billion original: "kharva", hundred-billion original: "nikharva", trillion original: "mahapadma", and ten-trillion original: "shanku"; following that, the "ocean" original: "jaladhi"; 10^14, the "last" original: "antya"; 10^15, the "middle" original: "madhya"; 10^16, and the "beyond-half" original: "parardha"; 10^17—were established by earlier teachers in sequence, each being ten times the previous, to facilitate the use of numbers. || 2 || 3 ||
Meaning: Unit, ten, hundred, thousand, ten-thousand, lakh, ten-lakh, crore, etc.—for the sake of mathematical transactions, the ancient teachers designated these names so that each subsequent place is ten times the value of the one before it. For example, ten is ten times one; a hundred is ten times ten; a thousand is ten times a hundred, and so on. || 2 || 3 ||
(Rule 1) The sum of the digits, or their difference, should be calculated according to their places, either in order or in reverse order.
Prose Order: The addition original: "yogah" or the difference original: "antaram" should be performed according to the specific place original: "yathasthanakam", either in direct order from right to left or in reverse order from left to right.
Meaning: Whether adding or subtracting, one must operate digit-by-digit according to their place value—that is, adding or subtracting the units to units, tens to tens, hundreds to hundreds, and so forth. This can be done starting from the first digit (units) or from the last digit (the highest place value).
The Problem: An example regarding addition and subtraction—
O dear child Lilavati, you who possess a clever mind, tell me the sum of these numbers: two, five, thirty-two, one hundred and ninety-three, eighteen, and ten.
Add a hundred to this sum, and then tell me the result after subtracting ten thousand, if you are skilled in the method of addition and subtraction.
Prose Order: O child! O wise Lilavati! If you are skilled in the logic of addition and subtraction original: "vyakte yukti-vyavakalana-marge", then tell me the sum of these: 2, 5, 32, 193, 18, and 10, increased by 100. Also, tell me the result when 10,000 original: "ayuta" is subtracted from it. || 1 ||