Exponential Form Calculator

Convert between standard notation and scientific/exponential notation. Find the mantissa and exponent instantly.

Select Conversion Direction

Enter any number: whole, decimal, negative, very large or very small.

Result

Exponential Form
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45600 ➔ 4.56 x 10^4
Standard Form ---
Scientific Notation ---
E-Notation ---
Mantissa (Coefficient) ---
Exponent (Power of 10) ---
Number of Significant Digits ---

Step-by-Step Conversion

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What is Exponential / Scientific Notation?

Scientific notation (also called exponential notation) is a way of expressing very large or very small numbers in a compact form. A number is written as the product of a coefficient (mantissa) between 1 and 10, and a power of 10. For example, 45,600 becomes 4.56 x 104.

The general form is: a x 10n, where 1 ≤ |a| < 10 and n is an integer.

Conversion Examples

Large Numbers

Move the decimal point left until only one digit remains before it.

45600 = 4.56 x 104

Small Numbers

Move the decimal point right until the first nonzero digit is before it.

0.00032 = 3.2 x 10-4

Negative Numbers

Apply the same rules, keeping the negative sign.

-678000 = -6.78 x 105

E-Notation

Computers use E-notation: mantissa followed by 'e' and the exponent.

4.56e4 = 4.56 x 104

Why Use Scientific Notation?

Scientific notation is essential in science, engineering, and computing because it makes extremely large or small numbers manageable. The speed of light (299,792,458 m/s) is more easily written as 2.998 x 108 m/s. The mass of an electron (0.000000000000000000000000000000911 kg) becomes 9.11 x 10-31 kg.

Key Terminology

  • Mantissa (Coefficient): The number between 1 and 10 in scientific notation.
  • Exponent: The power of 10 that indicates how many places to move the decimal.
  • E-Notation: Computer-friendly format where 'e' separates mantissa and exponent.
  • Significant Figures: The meaningful digits in the mantissa.

Tips for Converting

  • Count decimal places moved to determine the exponent.
  • Moving the decimal left gives a positive exponent (large numbers).
  • Moving the decimal right gives a negative exponent (small numbers).
  • The mantissa must be at least 1 but less than 10.
  • When converting back, move the decimal in the opposite direction.