Convert a Large Number
Enter a number or supported mathematical expression and choose the notation you want to use for the output.
What Is Large Number Notation?
Large number notation provides compact ways to represent values that would otherwise require enormous numbers of decimal digits. Scientific notation is useful for numbers with hundreds or thousands of digits, while hyperoperations and arrow notation describe values that grow much faster.
Scientific notation
Scientific notation expresses a number as a coefficient multiplied by a power of ten. It is useful for representing very large and very small values in a compact format.
a × 10n
For example, one million can be written as 1 × 106. A googol is 1 × 10100.
Powers and exponentiation
Exponentiation represents repeated multiplication. For example, 210 = 1,024. Much larger powers can be represented without writing out every decimal digit.
Tetration
Tetration is repeated exponentiation, often represented using double up-arrows. For example:
2 ↑↑ 3 = 222 = 16
Higher up-arrow notation
Knuth's up-arrow notation extends beyond exponentiation and tetration. Three arrows represent pentation, four arrows represent hexation, and additional arrows define further hyperoperation levels.
Supported Conversion Examples
| Input | Notation | Possible conversion |
|---|---|---|
1000000 |
Decimal | 1 × 10^6 |
1e100 |
Scientific | 1 × 10^100 |
10^100 |
Power | 1 × 10^100 |
2^10 |
Exponentiation | 1024 |
2^^5 |
Tetration | Symbolic or numerical when safely supported |
2^^^3 |
Pentation | Symbolic up-arrow notation |
Why Can't Every Large Number Be Converted to Decimal?
A number can be mathematically well-defined without being practical to display as a decimal expansion. Some numbers have more digits than could be stored or printed using ordinary computer resources.
Scientific notation can represent many enormous values compactly. However, even scientific notation is not always sufficient for numbers defined through repeated hyperoperations. For those expressions, symbolic notation preserves the mathematical definition without requiring an impossible decimal expansion.
Frequently Asked Questions
What is a large number notation converter?
It is a tool that changes how a number is represented. It can convert ordinary values into scientific notation, powers of ten, and selected symbolic representations.
Can I convert a googol into scientific notation?
Yes. A googol is exactly 10100, or 1 × 10100.
Can I convert Graham's number into decimal form?
Its complete decimal expansion is far too large to write or store in ordinary practical computing systems. It is represented using its mathematical definition and up-arrow notation instead.
What does the double up-arrow mean?
Double up-arrows represent tetration, which is repeated exponentiation. For example, 2 ↑↑ 3 represents 2 raised to the power of 2 raised to the power of 2, with the usual right-associated tower convention.
What is the difference between scientific notation and tetration?
Scientific notation represents a number using a coefficient and a power of ten. Tetration is a mathematical operation that repeatedly applies exponentiation and can create vastly larger numbers.
Does this converter support arbitrary-precision numbers?
No. It uses ordinary PHP floating-point calculations for supported numerical conversions. Expressions beyond its safe numerical range are retained symbolically.