Sumivo · Mathematics
Scientific Notation Calculator
Enter a decimal or E notation value to see all four forms. To convert a × 10^n back to decimal, enter a in the first field and n in the optional exponent field. Leave significant figures blank for an exact conversion.
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SCIENTIFIC NOTATION
1.23456 × 10^5
- Scientific notation
- 1.23456 × 10^5
- E notation
- 1.23456E5
- Engineering notation
- 123.456 × 10^3
- Decimal form
- 123456
Calculation trace
- 123456 = 1.23456 × 10^5Normalize the coefficient and apply optional significant-figure rounding
- 1.23456 × 10^5 = 1.23456E5Write the same power of ten with E
- 1.23456 × 10^5 = 123.456 × 10^3Choose an engineering exponent divisible by three
- 1.23456 × 10^5 = 123456Shift the decimal point without floating-point multiplication
How it works
For a nonzero input, the decimal point moves until the coefficient has magnitude at least 1 and less than 10; the exponent records that shift and the sign is kept. Digit strings preserve the decimal value exactly. If you request significant figures, the next digit determines rounding: 5 or above increases the retained magnitude, with ties away from zero. A carry can increase the exponent, so 999.9 at two significant figures becomes 1.0 × 10^3. Every displayed form uses that same rounded value. E notation replaces × 10^ with E. Engineering notation chooses the next lower multiple of three as its exponent. For reverse conversion, enter coefficient a and integer n; the tool shifts the decimal point for a × 10^n.
Assumptions & limits
- Accepts signed decimal strings and e/E notation, including surrounding spaces. Expressions, fractions, commas, NaN and Infinity are rejected. This tool converts notation; it does not evaluate arithmetic expressions.
- Exact mode preserves the value, not measurement precision inferred from trailing zeros. Optional precision is 1–100 significant figures, with ties rounded away from zero. Scientific and E forms retain requested trailing zeros; decimal form omits unnecessary fractional zeros. Engineering coefficients may need place-holding integer zeros.
- Each input is limited to 4096 characters and the coefficient to 2000 digits. Each supplied exponent and the normalized scientific exponent must be within −1000 to 1000, before and after rounding; exceeding a limit is rejected with a warning, never clamped. A valid engineering exponent may be −1002. Scientific exponents with magnitude at least 100 trigger a long-output warning.
- Zero, including negative zero, is shown as 0 × 10^0, 0E0 and decimal 0 regardless of requested precision. The usual nonzero coefficient rule does not apply to zero.
FAQ
- How do you write a number in scientific notation?
- Move the decimal point to leave one nonzero digit before it, and compensate with a power of ten. For example, 123456 = 1.23456 × 10^5. Keep a negative sign on the coefficient. Zero uses the explicit convention 0 × 10^0 here.
- What does a negative exponent mean?
- A negative power of ten means division by that power: 10^-3 = 1/1000. Thus 4.5 × 10^-4 = 0.00045. The exponent describes scale; the coefficient sign determines whether the number is negative.
- What is E notation on a calculator?
- E means times ten to a power: 1.2E5 is 1.2 × 10^5, or 120000. Either e or E is accepted here. In this notation the letter is a separator, not the mathematical constant e.
- What is the difference between scientific and engineering notation?
- Scientific notation keeps the nonzero coefficient magnitude between 1 inclusive and 10 exclusive. Engineering notation uses an exponent divisible by three and a coefficient magnitude from 1 inclusive to 1000 exclusive. For example, 0.00045 is 4.5 × 10^-4 or 450 × 10^-6.
- How do you add, subtract, multiply or divide scientific notation?
- For addition or subtraction, rewrite both terms with the same exponent before combining coefficients. For multiplication, multiply coefficients and add exponents. For division, divide coefficients and subtract exponents; the divisor must be nonzero. Normalize afterward and round only at the end. This converter does not perform those arithmetic operations.
Related calculators
SOURCES
- OpenStax, Rice UniversityPrealgebra 2e — 10.5 Integer Exponents and Scientific Notation ↗
Section 10.5: negative integer exponents, conversion between decimal and scientific notation, and multiplication and division using scientific notation. Engineering formatting, precision limits and rounding are calculator conventions.
Accessed 2026-10-02