Scientific Notation Converter

Convert numbers to and from scientific notation, E notation, engineering notation, and standard form.

Convert between scientific notation and standard form. Enter any number like 123000 or 2.5e3.

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help_outlineHow to Useexpand_more

Converting Numbers to Scientific Notation

This converter transforms numbers between scientific notation, E notation, engineering notation, standard form, and word form. Enter any number format and receive instant conversions to all other formats.

The Conversion Process:

  1. Move the decimal point until only one non-zero digit remains to the left
  2. Count how many places you moved the decimal - this becomes the exponent
  3. Moving left = positive exponent; moving right = negative exponent
  4. Write as a × 10^b (read as "a times 10 to the power of b")

Input Formats:

Enter numbers using standard notation (357096), scientific notation with carat (3.45 × 10^5), or E notation (3.45e5). The converter handles all formats automatically.

infoWhat is Scientific Notation Converter?expand_more

Scientific notation is a standardized way to express numbers where the coefficient (a) is between 1 and 10, multiplied by 10 raised to a power (b). The proper format is a × 10^b where 1 ≤ |a| < 10.

E notation (exponential notation) is the same as scientific notation but substitutes the letter "e" or "E" for "× 10^". For example, 3.57096 × 10^5 becomes 3.57096e5. This format is commonly used in calculators and programming.

The order of magnitude is identified by the exponent in standard form. For example, 3.4 × 10^5 has an order of magnitude of 5, since 10 is raised to the 5th power. This helps quickly compare the relative size of numbers.

functionsFormulaexpand_more

Scientific Notation Format:

a × 10^b where 1 ≤ |a| < 10

a = coefficient, b = exponent (power of 10)

Converting to Scientific Notation:

• Move decimal until one non-zero digit is left of decimal

• Count decimal places moved = exponent value

• Moved left → positive exponent

• Moved right → negative exponent

Converting to Standard Form:

Multiply coefficient by 10 raised to the exponent:

3.456 × 10^4 = 3.456 × 10,000 = 34,560

3.456 × 10^-4 = 3.456 × 0.0001 = 0.0003456

lightbulbExamplesexpand_more

Example 1: Convert 357,096 to Scientific Notation

Move decimal 5 places to the left: 3.57096

Moved left, so exponent is positive: b = 5

Result: 3.57096 × 10^5 (or 3.57096e5)

Example 2: Convert 0.005600 to Scientific Notation

Move decimal 3 places to the right: 5.600

Moved right, so exponent is negative: b = -3

Result: 5.600 × 10^-3 (trailing zeros preserved)

Notation Equivalents Table

StandardScientificE Notation3570963.57096×10⁵3.57096e50.000989.8×10⁻⁴9.8e-4
quizFAQexpand_more
What's the difference between scientific notation and E notation?expand_more
They represent the same value. Scientific notation uses '× 10^' with a superscript exponent (3.57 × 10^5), while E notation uses 'e' followed by the exponent (3.57e5). E notation is preferred for calculators and computer input since it doesn't require special formatting.
How do I determine the order of magnitude?expand_more
The order of magnitude is simply the exponent in scientific notation. For 3.4 × 10^5, the order of magnitude is 5. This tells you the number is in the hundred-thousands range. Each increase of 1 in order of magnitude means the number is 10 times larger.
What about trailing zeros after the decimal?expand_more
Trailing zeros to the right of the decimal point are significant figures and should be preserved. For example, 0.005600 becomes 5.600 × 10^-3, not 5.6 × 10^-3. However, trailing zeros to the left of the decimal (like in 357000) may or may not be significant depending on context.
How do negative exponents work?expand_more
A negative exponent indicates the number is less than 1. Each negative power of 10 moves the decimal one place to the left: 10^-1 = 0.1, 10^-2 = 0.01, 10^-3 = 0.001. So 5.6 × 10^-3 = 0.0056.
When is scientific notation most useful?expand_more
Scientific notation is essential for very large numbers (astronomical distances, molecular counts) or very small numbers (atomic sizes, wavelengths). It makes calculations easier by separating the magnitude (exponent) from the precision (coefficient) and clearly shows significant figures.