#1,084 – Representing Numbers Using Scientific Notation

We often represent numbers (especially floating point numbers) using something called scientific notation.

With scientific notation (in base 10), you represent a number using the form:

The a term is known as the significand, or mantissa and the b term is known as the exponent.

Scientific notation is useful because it allows easily writing very large or very small numbers by using the exponent to avoid writing a bunch of extra zeroes.

We also typically write the number so that the significand only has one significant digit, that is–one digit to the left of the decimal point.  (This is known as normalized form).

For example:

Notice that we can now write very large and very small numbers fairly concisely:

We only need to write down the numbers’ significant digits (i.e. significand), that is–the non-zero digits that contribute to the number’s precision.  (Zeroes between non-zeroed digits are also significant).