Using Scientific Notation

How many stars do you see in Figure 11? There are too many to count. Scientists often work with very large or very small numbers. For example, the speed of light is about 300,000,000 meters per second. On the other hand, an average snail has been clocked at a speed of only 0.00086 meter per second.

Figure 11 Scientists estimate that there are more than 200 billion stars in the Milky Way galaxy. Applying Concepts What is this number in scientific notation?

Instead of having to write out all the zeroes in these numbers, you can use a shortcut called scientific notation. Scientific notation is a way of expressing a value as the product of a number between 1 and 10 and a power of 10. For example, the number 300,000,000 written in scientific notation is $3.0 \times {10}^8$. The exponent, 8, tells you that the decimal point is really 8 places to the right of the 3.

For numbers less than 1 that are written in scientific notation, the exponent is negative. For example, the number 0.00086 written in scientific notation is $8.6 \times {10}^{-4}$. The negative exponent tells you how many decimals places there are to the left of the 8.6. Scientific notation makes very large or very small numbers easier to work with.