Scientific Notation Calculator

Understanding scientific notation for students and professionals

Scientific notation expresses numbers as m × 10^n, where the mantissa m is between 1 and 10 in absolute value, and n is an integer exponent. This compact form makes very large or very small quantities easy to read, compare, and compute, especially in science, engineering, finance, and data analysis.

Why scientific notation matters

• Clarity: Avoids long strings of zeros for extremes (e.g., 0.00000032 → 3.2 × 10^-7).
• Precision: Reports only meaningful digits using significant figures.
• Consistency: Standardizes values across units, sensors, and instruments.

Mantissa, exponent, and normalization

To normalize, shift the decimal so the mantissa has one non-zero digit before the decimal point, then update the exponent accordingly. For example, 12,300 becomes 1.23 × 10^4; 0.0012 becomes 1.2 × 10^-3. Negative numbers retain their sign on the mantissa.

Significant figures and rounding

Significant figures represent the certainty in measured or computed values. Rounding the mantissa to a fixed number of significant figures keeps results consistent. For instance, with 3 sig figs, 6.022 × 10^23 rounds to 6.02 × 10^23.

Operations in scientific notation

• Add/Subtract: Convert to standard numbers or align exponents before combining; then renormalize.
• Multiply: Multiply mantissas and add exponents, then renormalize to keep 1 ≤ |m| < 10.
• Divide: Divide mantissas and subtract exponents, then renormalize similarly.

Best practices

• Declare sig figs: State the significant figures used in reporting.
• Match context: Scientific papers often use scientific or engineering notation; spreadsheets prefer e notation.
• Check units: Keep units consistent when performing operations to avoid interpretation errors.

Frequently asked questions

HOW TO convert a number to scientific notation?

Steps: Enter the number in A, select “Convert A ↔ Scientific,” choose your significant figures, and click Calculate.

HOW TO convert scientific notation back to a standard number?

Enter a value like 3.2e-7 or 3.2 × 10^-7 in A, choose Standard number as output, and calculate.

HOW TO set significant figures correctly?

Use the Significant figures input (e.g., 3 or 6). The mantissa is rounded to that precision in the final result.

HOW TO add numbers in scientific notation?

Fill A and B, choose A + B, set sig figs, and calculate. The tool aligns exponents, computes, and renormalizes.

HOW TO multiply or divide scientific numbers?

Select A × B or A ÷ B. The tool multiplies/divides mantissas, updates exponents, and normalizes the result.

HOW TO use engineering notation?

Pick Engineering as output format to force exponents to multiples of 3 (e.g., k, M, μ scales), then calculate.

HOW TO copy the result?

Click Copy result to place the formatted output on your clipboard for reports or spreadsheets.

HOW TO embed this calculator on my website?

Copy this single-file HTML page into your project, link it from navigation, or embed via iframe with a descriptive title.