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Normal form (Scientific notation)

Normal form (scientific notation) is a way to write very large or very small numbers in a more compact form. It has two parts:

  • A number, usually in the range 0 - 10, called the coefficient.
  • A power of ten to multiply it by called the exponent.

Big numbers

For example the distance to the sun is about 93,000,000 miles. In scientific notation.

93,000,000 would be written 93×106
106 is one million (One way to remember this is 106 is one with six zeros after it.) So the notation simply means 93 times one million.

Very small numbers too

The diameter of a human hair is about 60 millionths of a meter. Or .00005 meters. We can write this as

50 × 10-6
Recall that So
50 × 10-6    is 50 times one millionth.

In science and engineering

In science and engineering the exponent is often made a multiple of 3. This is because the units are often quoted that way. For example we have electric power measures in watts. 1000 watts is called a kilowatt. One million volts is called a megawatt. So the coefficient is often adjusted to make the exponent 1000, or 1,000,000.

So using watts as an example:

50 = 50 watts
50 × 103 = 50 kilowatts
50 × 106 = 50 megawatts
It is done on small values too
50 × 10-3 = 50 milliwatts

In computers and calculators

Because it is hard to write in a computer program and display in calculators, this form is often written in "E" format. So for example

  • 50 × 106 would be written as 50E6.
  • 3 × 10-6 would be written as 3E-6.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values