# 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.

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