Scientific Notation (Basic science review)

There are words in English for big numbers, such as million, billion, even trillion. A trillion is 1,000,000,000,000. That’s a 1 with 12 zeroes behind it.

However, scientists and engineers often use numbers that are much bigger than this. It can be difficult to write out numbers that big. Not only do they take up space and time to write them down, but it is also difficult to determine what the number is or to compare them to other numbers.

Because of this, scientists use scientific notation to write very large numbers. Scientific notation uses a number called an “exponent” to indicate how many zeroes are following the 1.

For instance, 1,000,000,000,000 can be written as 10¹². This is much quicker and simpler to write and also tells you how many zeroes there are without having to count them.

The exponent isn’t just a count of the number of zeroes. The number actually shows how many times a number is multiplied by itself. For instance, 4³ = 4×4×4 = 64. 10² = 10×10 = 100, 10³ = 10×10×10 = 1000, etc. It turns out that multiplying by 10 is the same as putting another zero after the 1.

A number like 4,000,000 can be thought of as 4 x 1,000,000 and can therefore be written as 4 x 10⁶.

A number like 4,256,000 can be thought of as 4.256 x 1,000,000 and can be written as 4.256 x 10⁶.