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:
- Move the decimal point left until you have a number between 1 and 10
- Count how many places you moved (this is your positive exponent)
- Write: coefficient × 10^(number of places)
Example: 6,500,000 = 6.5 × 10⁶
For small numbers:
- Move the decimal point right until you have a number between 1 and 10
- Count how many places you moved (this is your negative exponent)
- 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
6.5e6or6.5E6 - 4.5 × 10⁻⁴ is written as
4.5e-4or4.5E-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
| Value | Scientific Notation | Description |
|---|---|---|
| 299,792,458 | 2.998 × 10⁸ | Speed of light (m/s) |
| 6.022 × 10²³ | 6.022 × 10²³ | Avogadro's number |
| 0.000000001 | 1 × 10⁻⁹ | Nano (billionth) |
| 1,000,000,000 | 1 × 10⁹ | Giga (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.
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