Convert between standard and scientific notation
Scientific notation is a way to write very large or very small numbers compactly. It's used by scientists to talk about everything from the distance to stars to the size of an atom without writing out a ton of zeros!
Concept
Scientific notation expresses a number as the product of a number between 1 and 10 and a power of 10. **The Format: a x 10ⁿ** * **a:** A number such that 1 ≤ |a| < 10. This is called the coefficient. * **n:** An integer exponent. **1. Converting from Standard Form to Scientific Notation** **For Large Numbers (>10):** 1. Move the decimal point to the **left** until you have a number between 1 and 10. 2. Count how many places you moved the decimal. This will be your **positive** exponent. * **Example: 345,000** 1. Move the decimal from the end (345000.) to between the 3 and 4 (3.45). 2. You moved it **5 places** to the left. 3. Result: **3.45 x 10⁵** **For Small Numbers (<1):** 1. Move the decimal point to the **right** until you have a number between 1 and 10. 2. Count how many places you moved the decimal. This will be your **negative** exponent. * **Example: 0.0078** 1. Move the decimal from its current position to between the 7 and 8 (7.8). 2. You moved it **3 places** to the right. 3. Result: **7.8 x 10⁻³** **2. Converting from Scientific Notation to Standard Form** **For Positive Exponents:** Move the decimal point to the **right** the number of places indicated by the exponent, adding zeros as needed. * **Example: 5.2 x 10⁴** 1. The exponent is 4. Move the decimal 4 places right. 2. 5.2 -> 52. -> 520. -> 5200. -> 52000. 3. Result: **52,000** **For Negative Exponents:** Move the decimal point to the **left** the number of places indicated by the exponent, adding zeros as needed. * **Example: 8.1 x 10⁻³** 1. The exponent is -3. Move the decimal 3 places left. 2. 8.1 -> .81 -> .081 -> .0081 3. Result: **0.0081** **Key Idea:** * **Positive exponent:** Big number. * **Negative exponent:** Small number (a decimal fraction). * The exponent tells you the number of places to move the decimal.
Try it
Practice: Convert between standard and scientific notation.