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Scientific Notation Calculator

Decimal → Scientific Notation

Scientific Notation → Decimal

Understanding Scientific Notation

Format: Scientific notation expresses numbers as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer.

Large numbers: 6,500,000 = 6.5 × 10⁶

Small numbers: 0.00045 = 4.5 × 10⁻⁴

E-notation: Used in computers, 6.5e6 means 6.5 × 10⁶

What is Scientific Notation?

Scientific notation is a way of expressing very large or very small numbers in a compact form. It is widely used in science, engineering, and mathematics.

The Format

A number in scientific notation is written as: a × 10ⁿ

  • a (coefficient): A number where 1 ≤ |a| < 10
  • n (exponent): An integer indicating the power of 10

Converting to Scientific Notation

For large numbers:

  1. Move the decimal point left until you have a number between 1 and 10
  2. Count how many places you moved (this is your positive exponent)
  3. Write: coefficient × 10^(number of places)

Example: 6,500,000 = 6.5 × 10⁶

For small numbers:

  1. Move the decimal point right until you have a number between 1 and 10
  2. Count how many places you moved (this is your negative exponent)
  3. Write: coefficient × 10^(-number of places)

Example: 0.00045 = 4.5 × 10⁻⁴

E-Notation

Computers often use E-notation (or exponential notation) as an alternative:

  • 6.5 × 10⁶ is written as 6.5e6 or 6.5E6
  • 4.5 × 10⁻⁴ is written as 4.5e-4 or 4.5E-4

Arithmetic Operations

Multiplication

Multiply coefficients and add exponents:

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

Division

Divide coefficients and subtract exponents:

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10⁽ᵐ⁻ⁿ⁾

Addition & Subtraction

First align the exponents, then add or subtract the coefficients:

(a × 10ⁿ) + (b × 10ⁿ) = (a + b) × 10ⁿ

Common Examples

ValueScientific NotationDescription
299,792,4582.998 × 10⁸Speed of light (m/s)
6.022 × 10²³6.022 × 10²³Avogadro's number
0.0000000011 × 10⁻⁹Nano (billionth)
1,000,000,0001 × 10⁹Giga (billion)

Frequently Asked Questions

How do I convert a number to scientific notation?+

Move the decimal point until exactly one nonzero digit remains to its left, then count the places moved. Moving left gives a positive exponent (6,500,000 = 6.5 × 10⁶); moving right gives a negative one (0.00045 = 4.5 × 10⁻⁴). Type any decimal into the Convert tab and the calculator shows the scientific and E-notation forms instantly.

What is E-notation and how do I read 3.5e-4?+

E-notation is the computer-friendly version of scientific notation where 'e' means 'times ten to the power of'. So 3.5e-4 means 3.5 × 10⁻⁴ = 0.00035, and 6.5E6 means 6.5 × 10⁶ = 6,500,000. The calculator accepts both formats as input, including the caret style 3.5 × 10^-4.

How do I multiply or divide numbers in scientific notation?+

For multiplication, multiply the coefficients and add the exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. For division, divide the coefficients and subtract the exponents. If the resulting coefficient falls outside 1–10, the calculator renormalizes it — for example 50 × 10⁵ becomes 5 × 10⁶.

Why do we add or subtract exponents only after aligning them?+

Addition and subtraction only work on like terms, so both numbers must share the same power of ten first. To compute 4.2 × 10⁵ + 3 × 10⁴, rewrite the second as 0.3 × 10⁵, giving 4.5 × 10⁵. The calculator handles this alignment automatically in Calculate mode.

Is this scientific notation calculator free and mobile-friendly?+

Yes. It is free, requires no sign-up, and all conversion and arithmetic runs entirely in your browser — nothing is transmitted to a server. It works on phones and tablets, which makes it handy for chemistry, physics, and astronomy homework anywhere.