The Exponential Notation

hack3rcon · June 25, 2023, 9:59am

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

Thank you.

jbe · June 25, 2023, 10:05am

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.

hax10 · June 25, 2023, 10:22am

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

github.com

rust-lang/rust/blob/3c5d71a99dd5ece7f6c87ca80b0adb1637c3b11a/library/core/src/num/dec2flt/parse.rs#L73


      
                          break;
                      }
                  } else {
                      break;
                  }
              }
          
              *s_ref = s;
          }
          
          /// Parse the scientific notation component of a float.
          fn parse_scientific(s_ref: &mut &[u8]) -> Option<i64> {
              let mut exponent = 0i64;
              let mut negative = false;
          
              let mut s = *s_ref;
          
              if let Some((&c, s_next)) = s.split_first() {
                  negative = c == b'-';
                  if c == b'-' || c == b'+' {
                      s = s_next;

hack3rcon · June 25, 2023, 10:28am

Hello,
Thank you so much for your reply.
Can you explain 12e-6 too?

jbe · June 25, 2023, 10:34am

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.