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Scientific Notation Calculator — Convert & Calculate

Convert numbers to scientific, E, and engineering notation, or perform add/subtract/multiply/divide arithmetic directly in scientific notation.

Updated
Scientific Notation
3.4 × 10^5
E Notation
3.4E5
Engineering Notation
340 × 10^3

Scientific notation: a × 10ⁿ where 1 ≤ |a| < 10. Engineering notation: same form but the exponent is always a multiple of 3, aligning with metric prefixes (kilo, mega, milli, etc.). For multiplication/division, mantissas multiply/divide and exponents add/subtract. For addition/subtraction, exponents must first be matched before the mantissas combine.
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Reference Values

Last verified:
Category Range What It Means Status
Scientific Notation ★ a × 10ⁿ, where 1 ≤ |a| < 10 The standard form — mantissa (a) is always between 1 and 10, exponent (n) can be any integer. Example: 3.4 × 10⁵. ★ Best
E Notation aEn (same value, calculator/programming format) Identical to scientific notation but written without the '×10' — common on calculators and in programming languages. Example: 3.4E5. Good
Engineering Notation a × 10ⁿ, where n is always a multiple of 3 Groups exponents to align with metric prefixes (kilo, mega, milli, micro) — mantissa can range from 1 to under 1000. Example: 340 × 10³ instead of 3.4 × 10⁵. Okay
Standard (Decimal) Notation The full expanded number Ordinary decimal form — becomes unwieldy for very large or very small numbers, which is exactly why scientific notation exists. Okay

Source: Standard mathematical notation conventions (scientific, engineering, and E notation)

Worked Examples

Convert 340,000 to Scientific Notation

Decimal Number
340000
3.4 × 10⁵ (Scientific) · 3.4E5 (E Notation) · 340 × 10³ (Engineering)

Move the decimal point until only one non-zero digit remains before it (3.4), then count how many places it moved (5) — that's the exponent.

Convert 0.000521 to Scientific Notation

Decimal Number
0.000521
5.21 × 10⁻⁴

For numbers smaller than 1, the exponent is negative — the decimal point moved 4 places to the right to reach 5.21.

Multiply: (3.4 × 10⁵) × (2 × 10³)

Number 1
3.4 × 10⁵
Number 2
2 × 10³
Operation
Multiply
6.8 × 10⁸

Multiply the mantissas (3.4 × 2 = 6.8) and add the exponents (5 + 3 = 8).

Add: (5 × 10⁶) + (3 × 10⁵)

Number 1
5 × 10⁶
Number 2
3 × 10⁵
Operation
Add
5.3 × 10⁶

Addition and subtraction require matching exponents first: 3 × 10⁵ = 0.3 × 10⁶, so 5 × 10⁶ + 0.3 × 10⁶ = 5.3 × 10⁶.

How to Use This Calculator

  1. 1

    Choose Convert or Arithmetic mode

    Convert Number turns a decimal into scientific/E/engineering notation. Arithmetic performs math directly on two numbers already in scientific notation.

  2. 2

    Enter your number(s)

    For conversion, type any decimal number. For arithmetic, enter each number's mantissa and exponent separately.

  3. 3

    For arithmetic, select the operation

    Add, subtract, multiply, or divide — the calculator handles exponent matching or combining automatically.

  4. 4

    Read the result

    Conversion mode shows all three notation formats at once. Arithmetic mode shows the result in scientific notation plus its full decimal equivalent.

What Each Value Means

Scientific Notation (a × 10ⁿ)
A way of writing numbers as a × 10ⁿ, where the mantissa (a) is always between 1 and 10 (exclusive of 10) and n is any integer — used to compactly represent very large or very small numbers.
Engineering Notation (a × 10ⁿ (n divisible by 3))
A variant of scientific notation where the exponent is always a multiple of 3, aligning directly with metric unit prefixes (kilo = 10³, mega = 10⁶, milli = 10⁻³, etc.).

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Frequently Asked Questions

How do you convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit remains to its left, then count how many places it moved — that count becomes the exponent. For 340,000: move the decimal 5 places left to get 3.4, so it's 3.4 × 10⁵. For numbers smaller than 1, the exponent is negative — 0.000521 becomes 5.21 × 10⁻⁴ (decimal moved 4 places right).
What is the difference between scientific notation, E notation, and engineering notation?
They represent the same value differently. Scientific notation writes it as a × 10ⁿ with the mantissa between 1 and 10 (3.4 × 10⁵). E notation is the same thing without the '×10' — common on calculators and in programming (3.4E5). Engineering notation keeps the exponent as a multiple of 3, aligning with metric prefixes like kilo and mega, so the mantissa can range up to just under 1000 (340 × 10³ instead of 3.4 × 10⁵).
How do you multiply or divide numbers in scientific notation?
Multiply or divide the mantissas normally, then add (for multiplication) or subtract (for division) the exponents. For (3.4 × 10⁵) × (2 × 10³): multiply mantissas (3.4 × 2 = 6.8) and add exponents (5 + 3 = 8), giving 6.8 × 10⁸.
How do you add or subtract numbers in scientific notation?
Unlike multiplication, addition and subtraction require matching exponents first — you can't directly add the mantissas of numbers with different powers of 10. For (5 × 10⁶) + (3 × 10⁵): rewrite 3 × 10⁵ as 0.3 × 10⁶ to match exponents, then add the mantissas: 5 + 0.3 = 5.3, giving 5.3 × 10⁶.
Why is engineering notation useful compared to standard scientific notation?
Because its exponents are always multiples of 3, engineering notation aligns directly with metric unit prefixes — 10³ is kilo, 10⁶ is mega, 10⁻³ is milli, 10⁻⁶ is micro, and so on. This makes it especially convenient in electrical engineering, physics, and any field working heavily with metric-prefixed units, since the exponent tells you the prefix directly.

References & Sources

  1. [1]
    NIST — SI Prefixes and Powers of 10 (opens in new tab)

    Supports: Evidence used for scientific notation glossary: mantissa, exponent & notation types, including related formulas, definitions, or reference values.

    Verified

  2. [2]
    NASA — Solar System Exploration: By the Numbers (opens in new tab)

    Supports: Evidence used for real-world examples of scientific notation, including related formulas, definitions, or reference values.

    Verified

  3. [3]
    Khan Academy — Scientific Notation (opens in new tab)

    Supports: Evidence used for scientific notation glossary: mantissa, exponent & notation types, including related formulas, definitions, or reference values.

    Verified

  4. [4]
    Khan Academy — Scientific Notation Examples (opens in new tab)

    Supports: Evidence used for how to convert decimal numbers to scientific notation, including related formulas, definitions, or reference values.

    Verified