--- title: 3.6 Scientific Notation description: Scientific notation is a compact way of writing very large or very small numbers. Instead of writing many zeros, scientific notation expresses a number using a coefficient multiplied by a power of 10. In Python, scientific notation is written using… url: "https://edcret.in/docs/python-programming/numeric-data-types-python/3-6-scientific-notation/" updated: "2026-07-29" category: Python Programming / Numeric Data Types --- # 3.6 Scientific Notation Scientific notation is a compact way of writing very large or very small numbers. Instead of writing many zeros, scientific notation expresses a number using a coefficient multiplied by a power of 10. In Python, scientific notation is written using the letter `e` or `E`. The general form is: ``` coefficienteexponent ``` For example: - `3.5e4` means `3.5 × 10⁴` - `2.1e-3` means `2.1 × 10⁻³` Scientific notation is commonly used in science, engineering, electronics, and mathematics where extremely large or very small values are frequently encountered. --- ## Syntax ``` variable_name = coefficienteexponent ``` ### Components | Component | Description | | --- | --- | | `variable_name` | Name of the variable. | | `coefficient` | A decimal number. | | `e` or `E` | Indicates "multiply by 10 raised to the power". | | `exponent` | Integer exponent that determines how many places the decimal point moves. | --- ## Example 1: Positive Exponent **main.py** ``` number = 3.5e4 print(number) print(type(number)) ``` ### Output ``` 35000.0 ``` ### Explanation - `3.5e4` means `3.5 × 10⁴`. - The decimal point moves four places to the right. - Scientific notation always produces a floating-point value. --- ## Example 2: Negative Exponent **main.py** ``` number = 2.5e-3 print(number) ``` ### Output ``` 0.0025 ``` ### Explanation - `2.5e-3` means `2.5 × 10⁻³`. - The decimal point moves three places to the left. - This notation is useful for representing very small numbers. --- ## Example 3: Using Uppercase `E` **main.py** ``` number = 7.2E5 print(number) ``` ### Output ``` 720000.0 ``` ### Explanation - Python accepts both lowercase `e` and uppercase `E`. - Both represent scientific notation. - The stored value is identical. --- ## Example 4: Checking the Data Type **main.py** ``` number = 9e2 print(number) print(type(number)) ``` ### Output ``` 900.0 ``` ### Explanation - Even though the result is a whole number (`900`), Python stores it as a floating-point number because scientific notation always creates a `float`. --- ## Example 5: Scientific Notation in Calculations **main.py** ``` distance = 1.5e6 time = 2 speed = distance / time print(speed) ``` ### Output ``` 750000.0 ``` ### Explanation - Scientific notation can be used just like any other numeric value. - Python performs arithmetic operations normally. - The result is a floating-point number. --- ## Example 6: Very Small Scientific Value **main.py** ``` charge = 1.6e-19 print(charge) ``` ### Output ``` 1.6e-19 ``` ### Explanation - Scientific notation is especially useful for representing extremely small values. - Python automatically displays the value using exponential notation. --- ## Example 7: Converting Scientific Notation to Integer **main.py** ``` number = int(5e3) print(number) print(type(number)) ``` ### Output ``` 5000 ``` ### Explanation - `5e3` is initially stored as a floating-point value. - The `int()` function converts it into an integer. - After conversion, the data type becomes `int`. --- ## Example 8: Scientific Notation in Expressions **main.py** ``` result = 2e3 + 5e2 print(result) ``` ### Output ``` 2500.0 ``` ### Explanation - `2e3` represents `2000.0`. - `5e2` represents `500.0`. - Python adds the two floating-point values. --- ## Example 9: Comparing Scientific Notation **main.py** ``` print(1e3 == 1000) ``` ### Output ``` True ``` ### Explanation - `1e3` represents `1000.0`. - Python compares `1000.0` with `1000`. - Since the numeric values are equal, the result is `True`. --- ## Example 10: Scientific Notation from User Input **main.py** ``` number = float(input("Enter a number in scientific notation: ")) print(number) ``` ### Sample Input ``` 6.02e23 ``` ### Output ``` 6.02e+23 ``` ### Explanation - The user enters a number in scientific notation. - `float()` converts the input string into a floating-point value. - Python prints the equivalent floating-point number. --- # Common Mistakes ### 1. Forgetting the Exponent **Incorrect** ``` number = 2.5e ``` ### Output ``` SyntaxError: invalid decimal literal ``` **Reason** Scientific notation requires an exponent after `e` or `E`. **Correct** ``` number = 2.5e3 ``` --- ### 2. Assuming Scientific Notation Produces an Integer **Incorrect** ``` number = 5e2 print(type(number)) ``` ### Incorrect Expectation ``` ``` ### Actual Output ``` ``` **Reason** Scientific notation always creates a floating-point value. --- ### 3. Using Multiple Decimal Points **Incorrect** ``` number = 2.5.3e4 ``` ### Output ``` SyntaxError: invalid syntax ``` **Reason** A numeric literal can contain only one decimal point. --- ### 4. Writing Spaces Inside Scientific Notation **Incorrect** ``` number = 3.5 e4 ``` ### Output ``` SyntaxError: invalid syntax ``` **Reason** There must be no spaces between the coefficient, `e`, and the exponent. --- # Best Practices - Use scientific notation for extremely large or very small numbers. - Use lowercase `e` consistently for better readability. - Remember that scientific notation values are stored as floating-point numbers. - Use `int()` if an integer value is required after computation. - Use meaningful variable names when storing scientific values. --- # Key Points to Remember - Scientific notation provides a compact way to write very large or very small numbers. - Python uses `e` or `E` to represent powers of 10. - Positive exponents move the decimal point to the right. - Negative exponents move the decimal point to the left. - Scientific notation always produces a value of type `float`. - Scientific notation values can participate in arithmetic operations like any other numeric values. - Both lowercase `e` and uppercase `E` are valid in Python.