Sometimes powers of 10 are helpful for expressing quantities, especially very large or very small quantities.

For example, the United States Mint has made over 500,000,000,000 pennies. To understand this number we can look at the number of zeros to know it is equivalent to 500 billion pennies. Since 1 billion can be written as $10^9$, we can say that there are over $500\boldcdot 10^9$ pennies. 

Sometimes we may need to rewrite a number using a different power of 10. We can say that $500\boldcdot 10^9 = 5\boldcdot 10^{11}$. Since the factor $10^9$ was multiplied by 100 to get $10^{11}$, the factor of 500 was divided by 100 to keep the value of the entire expression the same.

The same is true for very small quantities. For example, a single atom of carbon weighs about 0.0000000000000000000000199 grams. If we write this as a fraction we get $\dfrac{199}{10,000,000,000,000,000,000,000,000}$. Using powers of 10, it becomes $199\boldcdot10^{\text-25}$, which is a lot easier to write!

Just as we did with large numbers, small numbers can be rewritten as an equivalent value with a different power of 10. In this example we can divide the factor 199 by 100 and multiply the factor $10^{\text-25}$ by 100 to get $1.99\boldcdot10^{\text-23}$.