# The Exponential Notation

Hello,
Can someone explain the exponential notation to me? For example, how does `13.5e9` become `13500000000`?

Thank you.

Note that in Rust, the scientific notation can only describe floats, not integers, so 13.5e9 isn't `13500000000` but `13500000000.0` (Playground).

The scientific notation is short for "times 10 to the power of…".

Thus `13.5e9` means "`13.5` times 10 to the power of 9". Ten to the power of nine is 1,000,000,000. And 13.5 times 1,000,000,000 is 13,500,000,000.

Also see Wikipedia on scientific notation.

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You can also refer to the Rust compiler's source code, which shows how it parses this exponential notation.

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Hello,
Can you explain `12e-6` too?

Yes, 10 to the power of −6 is 0.000001.

Basically:

10 to the power of −2 = 0.01
10 to the power of −1 = 0.1
any number to the power of 0 = 1
10 to the power of 1 = 10
10 to the power of 2 = 100
10 to the power of 3 = 1000

and so on.

A good rule to memorize the outcome of scientific notation is to assume that the decimal separator is moved.

For example:

`12e-6` is the same as:

• `1.2e-5`
• `0.12e-4`
• `0.012e-3`
• `0.0012e-2`
• `0.00012e-1`
• `0.000012e-0`
• `0.000012e0`
• `0.000012`

Usually, you can read `…e-6` as Mikro prefix in the metric system. For example 12 µm are equal to `12e-6` meter. Or 12 millimeter are equal to `12e-3` meter.

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