Multiplying numbers in scientific notation extends what we do when we multiply regular decimal numbers. For example, one way to find $(80)(60)$ is to view 80 as 8 tens and to view 60 as 6 tens. The product $(80)(60)$ is 48 hundreds or 4,800. Using scientific notation, we can write this calculation as $\displaystyle (8 \times 10^1) (6 \times 10^1) = 48 \times 10^2$ 

To express the product in scientific notation, we would rewrite it as $4.8 \times 10^3$.

Calculating using scientific notation is especially useful when dealing with very large or very small numbers. For example, there are about 39 million, or $3.9 \times 10^7$ residents in California. The state has a water consumption goal of 42 gallons of water per person each day. To find how many gallons of water California would need each day if they met their goal, we can find the product $(42) (3.9 \times 10^7) = 163.8 \times 10^7$, which is equal to $1.638 \times 10^9$. That’s more than 1 billion gallons of water each day.

Comparing very large or very small numbers by estimation also becomes easier with scientific notation. For example, how many ants are there for every human? There are $5 \times 10^{16}$ ants and $8 \times 10^9$ humans. To find the number of ants per human, look at $\frac{5 \times 10^{16}}{8\times 10^9}$. Rewriting the numerator to have the number 50 instead of 5, we get $\frac{50 \times 10^{15}}{8 \times 10^9}$. This gives us $\frac{50}{8} \times 10^6$. Since $\frac{50}{8}$ is roughly equal to 6, there are about $6 \times 10^6$ or 6 million ants per person!