mathematics calculator
Scientific Notation Calculator
Convert a finite decimal number to a normalized coefficient multiplied by a power of ten.
Scientific Notation Calculator
Scientific notation
Enter a number to normalize it as a coefficient times a power of ten.
For nonzero values, the coefficient has an absolute value from 1 up to, but not including, 10.
Formula version 1.0.0
How to use this calculator
- Enter a finite decimal number.
- Select Calculate.
- Read the normalized coefficient and integer exponent.
- Confirm the coefficient times ten to the exponent reproduces the input.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
x | Input value | number |
a | Normalized coefficient | number |
n | Power-of-ten exponent | integer |
Checked examples
Large number
Inputs: 12,345
Calculation: Move the decimal four places left
Result: 1.2345 × 10⁴
The coefficient lies from 1 up to, but not including, 10.
Check: scientific-notation.test.ts
Small negative number
Inputs: −0.0042
Calculation: Move the decimal three places right
Result: −4.2 × 10⁻³
The sign stays with the coefficient and the exponent is negative.
Check: scientific-notation.test.ts
Assumptions, rounding, and limits
- The input is finite.
- Base ten is used.
- Nonzero output is normalized so 1 ≤ |a| < 10.
- Zero is represented as 0 × 10⁰.
Frequently asked questions
Why is the coefficient less than 10?
Normalized scientific notation keeps exactly one nonzero digit before the decimal point.
What does a negative exponent mean?
It represents repeated division by ten and is common for values between −1 and 1.
How is zero represented?
This calculator consistently reports 0 × 10⁰.
Sources and review
- OpenStax: Integer Exponents and Scientific Notation — Normalized scientific notation
- Formula version
- scientific.notation@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Finite real numbers represented in normalized base-ten notation.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.