10. What is scientific notation? How is it used to make working with numbers on a galactic or subatomic scale easier?

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Scientific notation is a method of writing numbers that are too large or too small to conveniently display in standard decimal form. In scientific notation, a number is written in the form

$$
a \times 10^n
$$

where:

- $$ a $$ is a coefficient such that $$ 1 \leq |a| < 10 $$.
- $$ n $$ is an integer representing the power of 10.

This notation is especially useful when working with numbers on a galactic or subatomic scale, for the following reasons:

1. **Simplicity and Clarity:**  
   It condenses long strings of zeros into a compact form. For example, instead of writing out $$ 1,000,000,000 $$, we can write it as $$ 1 \times 10^9 $$.

2. **Ease of Comparison:**  
   When numbers differ by many orders of magnitude, scientific notation helps quickly identify the relative scale by comparing the exponents. A distance such as $$ 2.5 \times 10^{20} $$ is immediately recognized as being far larger than a subatomic measurement like $$ 3.2 \times 10^{-15} $$.

3. **Simplified Computations:**  
   Multiplying and dividing numbers becomes easier because the rules of exponents apply. For instance, multiplying two numbers in scientific notation:

$$
   \left( a \times 10^n \right) \times \left( b \times 10^m \right) = (a \times b) \times 10^{n+m}
   $$

This eliminates the need to handle many zeros manually.

4. **Universal Application:**  
   Whether dealing with distances between galaxies or sizes of subatomic particles, scientific notation provides a consistent way to express values. For example:
   
   - The approximate diameter of the observable universe might be written as $$ 8.8 \times 10^{26} $$ meters.
   - The mass of a proton may be written as $$ 1.67 \times 10^{-27} $$ kilograms.

Overall, scientific notation is an indispensable tool in science and engineering as it simplifies the manipulation and comprehension of extremely large or small numbers.
Scientific notation is a way to write very large or very small numbers by expressing them as a number between 1 and 10 multiplied by a power of 10. This makes it easier to work with numbers on a galactic or subatomic scale by simplifying their representation and making calculations more manageable.

10. What is scientific notation? How is it used to make working with numbers on a galactic or subatomic scale easier?

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