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!

Do this: Read the concept below, then try the quiz or activity.

Lesson 27 of 188

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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.

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