Introduction:

In the field math that actually matters we rarely deal with numbers in the range of 1-100. Science likes to deal with number that are often too big for the human mind to comprehend. In the field of Chemistry a mole is the standard for the substance. A mole of apples would be 6,000,000,000,000,000,000,000 apples. In Astronomy the distance from the earth to the nearest star is 25,866,280,000,000 miles. Similarly on the other side of this totem pole is the field of biology with viruses ranging from 0.000000000004 to 0.000000000002 meter in length. From these two examples it is clear to see that when it comes to complex applications the notational system followed traditionally will simply not be enough. That is reason why the scientific community shifted to the exponential notation because it facilitated the expression of numbers far too big to be expressed in their entirety.

Explanation:

The exponential notation sometimes also known as the scientific notation is the use of the power of 10 for the representation of such large numbers. The positive and negative exponents for the representation of multiple and submultiples of 10. Using this exponential notation we keep things simple.

For example:

1000 meters would become 10×103, which simply means that 10x10x10=1000. This is valid for every calculation similar to this. 100 would become 10 x102 meaning 10×10=100.

By using these conventions we take the value of one mole apples and represent them as 6.02 x1023 apples. As for the distance to the nearest star, it becomes 25.8 x1015 miles and the size of a virus becomes 400 x10 -9.

Now a general rule is to maintain at least 3 significant figures before using the scientific notation. That is why you 25.8, 6.02 and 400 in all the examples discussed. Furthermore, a convention is used to determine that at which side the numeric part will move with the increase or decrease in the exponent. So if the exponent increases by some amount say x, the numeric part will move towards left, and if the exponent decreases by some amount say x, the numeric part will move towards right.