What is scientific and engineering notation?

Answer 1

Scientific notation is normally used for numbers that are either far to large or far to small to be written conveniently in decimal notation.A,B

For example the Earth's mass is approximately: 5,973,600,000,000,000,000,000,000.0 kg

In scientific notation this would be written as:

5.9736 x 1024 kg.

In normalised scientific notation numbers are written in the form:A,B

a x 10n

Where:

a is a number between 1 and 10

n is a positive or negative whole number.

In engineering notation, the n value is commonly in the form of multiples of 3. In this way the number will always explicitly match the corresponding SI prefixes.B

For example a distance of 50,000 m would be written as:

Scientific Notation: 5 x 104 m

Engineering notation: 50 x 103 m

In this example 103 corresponds to the SI prefix "kilo"C as such the engineering notation could be directly described verbally as "fifty kilometres" whereas scientific notation yields the much more unwieldy "five times ten to the power four metres" which is much less intuitively easy to understand, even though it is exactly the same distance.

Guidance on converting to and from scientific notation is given in the related links. Specifically References A and B.

References:

A Scientific notation - Engineering Maths Help from the 'mathcentre' Academic Website.

B Scientific notation: Wikipedia Entry.

C List of SI prefixes: Wikipedia Entry.

Please see related links.