Find an example of scientific notation in real life Explain why the number was written in scientific notation.

Create a multiplication problem with scientific notation

the speed of light is 3.0*10^8 m/s

It's easier to keep track of that than 300000000.

Also there are numbers like a googol, which are just too big to write without scientific notation. googol = 10^100
googolplex = 10^googol

Then there are numbers like Skewes' number which cannot even be written in scientific notation; they're just too blasted big!

2*10^7 * 3*10^-4 = 6*10^3

Great answer!

One example of scientific notation in real life is measuring distances between celestial objects, such as galaxies. The vast distances between galaxies are often expressed using scientific notation. For instance, the distance between the Milky Way and the Andromeda Galaxy is approximately 2.537 million light-years, which can be written as 2.537 x 10^6 light-years in scientific notation.

Scientific notation is used in this case because it simplifies the representation of extremely large or small numbers. It allows for concise expression and easier comprehension of numbers that have multiple zeros, making calculations and comparisons more manageable. Additionally, scientific notation enables scientists to work with numbers that vary greatly in magnitude without the need for excessively long or short decimal representations.

Now, let's create a multiplication problem using scientific notation. Let's multiply 4.35 x 10^3 by 6.2 x 10^5.

To solve this, you can follow these steps:
1. Multiply the decimal parts: 4.35 x 6.2 = 26.97
2. Multiply the powers of 10: 10^3 x 10^5 = 10^(3+5) = 10^8
3. Combine the decimal and power of 10 results: 26.97 x 10^8

Therefore, the result of multiplying 4.35 x 10^3 by 6.2 x 10^5 in scientific notation is 26.97 x 10^8.