Scientific Notation Calculator

Add, subtract, multiply and divide numbers in scientific notation, E notation or engineering notation.

Perform arithmetic with numbers in scientific notation, E notation, or standard form. Get step-by-step solutions with results in multiple formats.

First Number
×10
Second Number
×10
? × 10^?
Coefficient max 12 chars, exponent max 5
Try:
help_outlineHow to Useexpand_more

Performing Calculations with Scientific Notation

This calculator performs arithmetic operations on numbers expressed in scientific notation, E notation, or engineering notation. Enter values in any format and receive answers in all three notations for easy comparison.

Input Formats Accepted:

  • Scientific notation: 1.225 × 10⁵
  • E notation: 1.225e5 or 1.225E5
  • Standard notation: 122500
  • Decimal numbers: 0.001225

Operations Available:

Add, subtract, multiply, and divide numbers in any combination of formats. Results are automatically normalized so the coefficient falls between 1 and 10.

infoWhat is Scientific Notation Calculator?expand_more

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. This format is essential in science, engineering, and mathematics for handling extremely large or small numbers efficiently.

Standard Notation is the everyday way of writing numbers (like 122,500). Scientific Notation converts this to 1.225 × 10⁵. E Notation (exponential notation) writes this as 1.225e5, where "e" represents "times 10 to the power of."

This calculator handles all arithmetic operations while maintaining precision and automatically normalizing results. It's particularly useful for physics calculations, astronomical distances, molecular measurements, and any work involving very large or very small quantities.

functionsFormulaexpand_more

Multiplication:

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

Multiply coefficients, add exponents

Division:

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

Divide coefficients, subtract exponents

Addition & Subtraction:

Step 1: Convert both numbers to the same exponent

Step 2: Add or subtract the coefficients

Step 3: Normalize the result if needed

lightbulbExamplesexpand_more

Addition: 122500 + 3655

Convert to scientific: 1.225 × 10⁵ + 3.655 × 10³

Match exponents: 1.225 × 10⁵ + 0.03655 × 10⁵

Result: 1.26155 × 10⁵ (or 1.26155e5)

Multiplication: (3 × 10⁴) × (2 × 10³)

Multiply coefficients: 3 × 2 = 6

Add exponents: 4 + 3 = 7

Result: 6 × 10⁷ (or 6e7)

Division: (8 × 10⁶) ÷ (4 × 10²)

Divide coefficients: 8 ÷ 4 = 2

Subtract exponents: 6 - 2 = 4

Result: 2 × 10⁴ (or 2e4)

quizFAQexpand_more
What's the difference between scientific notation and E notation?expand_more
They represent the same value differently. Scientific notation uses '× 10' with a superscript exponent (like 1.225 × 10⁵), while E notation uses 'e' or 'E' followed by the exponent (like 1.225e5). E notation is commonly used in calculators and programming.
Why do I need to match exponents when adding or subtracting?expand_more
Just like adding fractions requires a common denominator, adding numbers in scientific notation requires the same power of 10. You can only add or subtract the coefficients when the exponents match. For example, 5 × 10³ + 3 × 10² becomes 5 × 10³ + 0.3 × 10³ = 5.3 × 10³.
What does 'normalizing' the result mean?expand_more
Normalizing ensures the coefficient is between 1 and 10 (standard scientific notation form). For example, if a calculation gives 25 × 10³, normalizing converts it to 2.5 × 10⁴ by moving the decimal point and adjusting the exponent accordingly.
Can I enter regular numbers instead of scientific notation?expand_more
Yes! You can enter whole numbers, integers, or decimals. The calculator will convert them to scientific notation automatically. For standard numbers, use a coefficient with exponent 0 (e.g., 5 × 10⁰ = 5).
How are significant figures handled?expand_more
This calculator preserves precision in calculations. For formal scientific work requiring specific significant figure rules, you may need to round your final answer according to the precision of your input values. The least precise measurement determines the significant figures in your answer.