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Scientific Notation Calculator

Convert any number to scientific, E-notation, engineering, and decimal formats — or perform arithmetic on two numbers and see the result in all four.

What Is Scientific Notation?

Scientific notation is a compact way to write very large or very small numbers. A number is in scientific notation when it is written as:

a × 10ⁿ

where 1 ≤ |a| < 10 (the coefficient has exactly one non-zero digit before the decimal point) and n is any integer.

Examples:

  • 93,000,000 = 9.3 × 10⁷
  • 0.000042 = 4.2 × 10⁻⁵
  • −5,600 = −5.6 × 10³

Scientific notation is standard in physics, chemistry, astronomy, and engineering — anywhere numbers span many orders of magnitude.

How to Convert to Scientific Notation

  1. Move the decimal point until exactly one non-zero digit sits to the left of it.
  2. Count the moves — that count becomes the exponent.
    • Moved left (number got smaller) → exponent is positive
    • Moved right (number got larger) → exponent is negative
  3. Write the result as coefficient × 10^exponent.

Example — large number: 93,000,000 → move decimal 7 places left → 9.3 × 10⁷

Example — small number: 0.000042 → move decimal 5 places right → 4.2 × 10⁻⁵

The Four Notation Formats

Scientific Notation

The standard form: coefficient between 1 and 10, multiplied by a power of 10. Example: 9.3 × 10⁷

E-Notation

Compact shorthand used in programming languages, spreadsheets, and scientific calculators. The letter E replaces × 10^ and the sign on the exponent is always explicit. Example: 9.3E+7

Engineering Notation

Like scientific notation, but the exponent is always a multiple of 3. This aligns with SI unit prefixes: 10⁻⁹ = nano, 10⁻⁶ = micro, 10⁻³ = milli, 10³ = kilo, 10⁶ = mega, 10⁹ = giga. The coefficient ranges between 1 and 1000. Example: 93 × 10⁶ (read as 93 megahertz rather than 9.3 × 10⁷ Hz)

Decimal

The fully expanded number with thousands separators where applicable. Example: 93,000,000

Arithmetic in Scientific Notation

Multiplication

Multiply the coefficients and add the exponents:

(a × 10ᵐ) × (b × 10ⁿ) = (a · b) × 10^(m + n)

Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷

Division

Divide the coefficients and subtract the exponents:

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10^(m − n)

Example: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴

Addition and Subtraction

Convert both numbers to the same exponent, then add or subtract the coefficients:

(3 × 10⁵) + (5 × 10⁴) = (3 × 10⁵) + (0.5 × 10⁵) = 3.5 × 10⁵

If the resulting coefficient falls outside 1–10, renormalize: 12 × 10⁴ = 1.2 × 10⁵.

Sources

Frequently Asked Questions

What is scientific notation?

Scientific notation expresses a number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. For example, 93,000,000 = 9.3 × 10⁷ and 0.000042 = 4.2 × 10⁻⁵. It is the standard way to write very large or very small numbers in science and engineering.

How do I enter a number in scientific notation format?

You can type numbers in decimal (e.g. 93000000), E-notation (e.g. 9.3e7), or with an explicit ×10^ (e.g. 9.3×10^7 — using × or x or *). The calculator parses all three formats automatically.

What is the difference between E-notation and scientific notation?

They represent the same value in different ways. Scientific notation writes 6.022 × 10²³, while E-notation writes 6.022E+23. E-notation is compact and is the format used in programming languages, calculators, and spreadsheets. The coefficient and exponent are identical in both formats.

What is engineering notation?

Engineering notation is a variant of scientific notation where the exponent is always a multiple of 3 (…−9, −6, −3, 0, 3, 6, 9…). This aligns with SI prefixes: 10⁻⁹ = nano, 10⁻⁶ = micro, 10⁻³ = milli, 10³ = kilo, 10⁶ = mega, 10⁹ = giga. The coefficient in engineering notation can be between 1 and 1000.

How do you multiply two numbers in scientific notation?

Multiply the coefficients and add the exponents: (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10^(m+n). For example, (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. If the product of the coefficients falls outside 1–10, adjust the exponent accordingly.