What is scientific notation?

Scientific notation expresses numbers as a × 10^n, where 1 ≤ |a| < 10 and n is an integer. It makes very large or very small numbers manageable. Example: 0.000456 = 4.56 × 10^−4; 6,020,000 = 6.02 × 10^6.

How do I convert a number to scientific notation?

Move the decimal point until you have a number between 1 and 10. Count the positions moved — right moves increase the exponent, left moves decrease it. Example: 0.00456 → move right 3 places → 4.56 × 10^−3.

What is E-notation and how does it differ from scientific notation?

E-notation is a compact computer-friendly format: 4.56e-3 means 4.56 × 10^−3. It is identical in value to scientific notation but easier to type without special characters. Most calculators and programming languages use E-notation.

How do you multiply numbers in scientific notation?

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n). Then normalise so the coefficient is between 1 and 10. Example: (3 × 10^4) × (2 × 10^3) = 6 × 10^7.

What is engineering notation?

Engineering notation is like scientific notation but restricts exponents to multiples of 3 (…−6, −3, 0, 3, 6…), aligning with SI prefixes (micro, milli, kilo, mega). Example: 0.000456 = 456 × 10^−6 (456 μ). This makes it easier to use metric prefixes.

Scientific Notation Calculator Online

Convert any number to scientific notation (a × 10^n) and E-notation instantly. See step-by-step conversion. Extended calculator adds arithmetic with full working steps. Professional mode supports batch conversion and engineering notation.

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Enter a Number

Enter any number — very large or very small.

Scientific Notation

4.56 × 10⁻⁴

E-Notation

4.56e-4

Coefficient (a)

4.56

Exponent (n)

-4

Original Number

0,000456

Conversion Steps

Move decimal right 4 places

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How to Use the Scientific Notation Calculator

Enter any number in the field above — it can be very large (like 602,200,000,000,000,000,000,000) or very small (like 0.000000000167). The calculator converts it to scientific notation (a × 10^n) and E-notation, with step-by-step instructions.

The Extended Calculator below adds an arithmetic tab for adding, subtracting, multiplying, and dividing numbers in scientific notation with full steps. The Professional Calculator provides batch conversion for multiple numbers and a reference table of scientific constants.

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Enter Number (decimal, fraction, or e-notation)

Scientific Notation

4.56 × 10^-4

E-Notation

4.56e-4

Coefficient

4.56

Exponent

-4

Standard Form

0,000456

Step-by-Step Conversion

1. Original: 0.000456

2. Move decimal right 4 places to get coefficient

3. Coefficient (a): 4.56 (must satisfy 1 ≤ |a| < 10)

4. Exponent (n): -4

5. Result: 4.56 × 10^-4

Scientific Notation Rules

Standard form: a × 10^n Where: 1 ≤ |a| < 10 (coefficient between 1 and 10) n is an integer (positive, negative, or zero) To convert: count decimal places moved Moved RIGHT → negative exponent (small numbers) Moved LEFT → positive exponent (large numbers) E-notation: aeN means a × 10^N (e.g. 4.56e-4)

Arithmetic Rules in Scientific Notation

Operation	Rule	Example
Multiplication	Multiply coefficients, add exponents	(3×10²) × (2×10³) = 6×10⁵
Division	Divide coefficients, subtract exponents	(6×10⁵) ÷ (2×10²) = 3×10³
Addition	Normalise exponents first, then add	3×10⁴ + 2×10³ = 3.2×10⁴
Subtraction	Normalise exponents first, then subtract	5×10⁶ − 3×10⁵ = 4.7×10⁶

Quick Reference: Common Numbers

Number	Scientific Notation	E-Notation
1,000	1 × 10³	1e+3
1,000,000	1 × 10⁶	1e+6
0.001	1 × 10⁻³	1e-3
602,200,000,000,000,000,000,000	6.022 × 10²³	6.022e+23
0.000000000167	1.67 × 10⁻¹⁰	1.67e-10
SA national debt (2025 est. R)	≈ 5.2 × 10¹²	5.2e+12

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Significant Figures

Notation Type

Numbers (one per line)

Input	Scientific Notation	E-Notation
0.000456	4.56 × 10^-4	4.56e-4
6020000000000000000000000	6.02 × 10^+24	6.02e+24
0.00000000167	1.67 × 10^-9	1.67e-9
9460730000000000000000	9.461 × 10^+21	9.461e+21

Frequently Asked Questions

Scientific notation writes numbers as a × 10^n where 1 ≤ |a| < 10. It makes extremely large or small numbers easier to read and compute. Example: the mass of Earth = 5.972 × 10²⁴ kg; a human hair width ≈ 7 × 10⁻⁵ m.

Move the decimal point until you have one non-zero digit to the left. Count the moves: if you moved left, the exponent is positive; if right, it is negative. 0.00456 → move right 3 → 4.56 × 10⁻³. 45,600 → move left 4 → 4.56 × 10⁴.

E-notation is a computer-typed shorthand: 4.56e-3 = 4.56 × 10⁻³. It is the same mathematically but avoids special characters. Used in most calculators, spreadsheets, and programming languages (Python, JavaScript, C, etc.).

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a×b) × 10^(m+n). If the resulting coefficient is ≥ 10 or < 1, adjust. Example: (4 × 10³) × (5 × 10⁴) = 20 × 10⁷ = 2 × 10⁸.

Engineering notation restricts exponents to multiples of 3, aligning with SI prefixes: 10⁻⁶ (micro), 10⁻³ (milli), 10³ (kilo), 10⁶ (mega). Example: 0.000456 = 456 × 10⁻⁶ = 456 μ. The Professional Calculator above converts to engineering notation.