Primary Mathematics/Scientific and engineering notation

Scientific and engineering notation

In science and engineering it is necessary to represent extremely small and large numbers. Representing such numbers with conventional notation becomes difficult, for numbers such as these:

123,456,000,000,000,000,000,000,000

0.000 000 000 000 000 000 000 000 000 000 378

One way to represent such numbers is using exponents. The first number, for example, could be represented as one of the following:

123,456 × 1021
123.456 × 1024
1.23456 × 1026
0.123456 × 1027

The second number could be represented as one of:

378 × 10-30
37.8 × 10-31
3.78 × 10-32
0.378 × 10-33

This notation is used to make extremely large and small numbers easier to write. It is composed of the base on the left, and the exponent (on the right).

Scientific notation

In scientific notation, the goal is to get the base number to be greater than or equal to 1.0, and less than 10. So, in the above examples, the two values in scientific notation were:

1.23456 × 1026

3.78 × 10-32

Engineering notation

Engineering notation is a variation of scientific notation, where the exponent is a multiple of 3, and the base is as close as possible to the range 0.1-1.0. In the above examples, the two values in engineering notation were:

0.123456 × 1027

0.378 × 10-33