Scientific Notation Calculator Convert between standard and scientific notation, perform calculations, and understand sig...

Scientific Notation Calculator

Convert between standard and scientific notation, perform calculations, and understand significant figures — with real-world examples.

Convert Notation

Arithmetic Operations

Significant Figures

Real Examples

Input Number

Convert To Scientific Notation Standard Notation Engineering Notation

Decimal Places

First Number

Second Number

Operation Addition (+) Subtraction (-) Multiplication (×) Division (÷)

Result Format Scientific Notation Standard Notation Engineering Notation

Significant Figures

Number

Operation Count Significant Figures Round to Significant Figures

Target Figures

Example Category Physics Constants Chemistry Astronomy Biology

Display Format Scientific Notation Standard Notation Both Formats

1.235 × 10⁵

123456.789

Original Value

1.235e5

Converted Value

6

Significant Figures

Scientific

Notation Type

Scientific Notation Rules

Scientific

a × 10ⁿ (1≤|a|<10)

Engineering

a × 10ⁿ (n multiple of 3)

Significant Figures

All digits except leading zeros

Conversion

Move decimal, count places

Interpretation

—

Exponent Visualization

Scientific Notation Fundamentals

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Standard Form**: a × 10ⁿ

• a (coefficient) is a number with absolute value between 1 and 10 (1 ≤ |a| < 10)
• n (exponent) is an integer

Engineering Notation**: Similar to scientific notation, but the exponent is always a multiple of 3, making it compatible with SI prefixes (kilo, mega, giga, etc.).

✅ Why Use Scientific Notation**:

• Concise representation of very large or small numbers
• Clear indication of significant figures
• Easier arithmetic operations
• Standard format in scientific and technical fields

Common Scientific Notation Mistakes

⚠️ Avoid these frequent errors:

• Incorrect coefficient range**: Coefficient must be 1-9.999..., not 0.5 or 15
• Significant figure errors**: Leading zeros don't count, trailing zeros after decimal do
• Exponent sign confusion**: Positive exponents for large numbers, negative for small
• Arithmetic mistakes**: Forgetting to align exponents before addition/subtraction
• Engineering notation**: Exponents must be multiples of 3 (..., -6, -3, 0, 3, 6, ...)

✅ Best Practices**:

• Always verify your coefficient is in the correct range
• Count significant figures before and after calculations
• For addition/subtraction, convert to same exponent first
• Use calculator's scientific notation mode when available

Real-World Applications

Scientific notation is essential in:

• Physics**: Speed of light (3.00 × 10⁸ m/s), Planck's constant (6.63 × 10⁻³⁴ J·s)
• Chemistry**: Avogadro's number (6.02 × 10²³ mol⁻¹), atomic masses
• Astronomy**: Astronomical distances (1.50 × 10¹¹ m to Sun), stellar masses
• Biology**: Cell sizes (1 × 10⁻⁵ m), DNA base pairs (3 × 10⁹ in human genome)
• Engineering**: Nanotechnology (1 × 10⁻⁹ m), electrical currents (1 × 10⁻³ A)

📊 Example Use Cases**:

• Physics**: Calculate force: F = (6.67×10⁻¹¹)(5.97×10²⁴)(7.35×10²²)/(3.84×10⁸)² = 1.98×10²⁰ N
• Chemistry**: Moles calculation: 2.5×10²⁴ molecules ÷ 6.02×10²³ mol⁻¹ = 4.15 mol
• Finance**: National debt: $3.14×10¹³ = $31,400,000,000,000

How to Use This Calculator

➡️ Convert Notation

"Convert 123456.789 to scientific notation" → 1.235 × 10⁵

➡️ Arithmetic Operations

"1.23e5 + 4.56e3" → 1.276 × 10⁵

➡️ Significant Figures

"Count sig figs in 0.00123450" → 6 significant figures

➡️ Real Examples

"Show physics constants" → Speed of light: 2.998 × 10⁸ m/s

Note: Supports standard input (123456), scientific notation (1.23e5), and engineering notation. Handles negative numbers and zero correctly.