Floating points are always stored in scientific notation. This means that a number like PI must be converted into scientific notation before we can use it. Lets look at the speed of light which is 3,000,000,00 m/s. This number is rarely seen in this form. We normally show it in its much more compact version of 3 x 10^8. This is known as scientific notation. Lets look at this number more carefully to see how we derive it from 3,000,000,00.

Looking at this number we can see that it has 8 zeros. Imagine there is a decimal point at the end of the 3,000,000,00. We can then move, or float, the point over to the left until we get 3. 00000000

We have moved the decimal point to the left by 8 places. In order to get the original number back we must multiply it by 1,000,000,00 or 10^8. The number of places we move the decimal point is the power we must raise 10 by. So if we move the decimal place by two, then we must raise 10 by 2. We raise 10 rather than any other number because denary numbers are in base 10. When we look at binary next we will use 2 because binary is in base 2.

We can also move the decimal point to the right. For example the number 0.000543 could be easily stored as 5.43 x 10^-4. We have moved the decimal 4 times to the right. As such we raise the 10 to the power of 4. However because it was moved to the right we say that we raise it to the negative four (-4). Whenever we move to the left we add the powers and whenever we move it to the right we substract the powers.

Mantissa and exponent

We are now ready to start making some definitions.

In order to recreate the number above we need to know three things.

• What base the number is in
• What the mantissa is
• What the exponent is

The mantissa is where the accuracy of the number is stored. The more digits here, the more accurate the number. The exponent is the magnitude of the number. A larger value means a larger number.