Scientific Notation

Very large and very small numbers are often expressed in scientific notation. In scientific notation, a number is written as the product of two numbers: a coefficient that is greater than or equal to one and less than ten, and 10 raised to a power. For example, the number 710,000 written in scientific notation is $7.1 \times {10}^5$. The coefficient in this number is 7.1. The power of ten, or the exponent, is 5. The exponent indicates how many times the coefficient must be multiplied by 10 to equal the number 710,000.

To convert a large number to scientific notation, move the decimal point to the left until it is located just to the right of the first nonzero number. The number of places that you move the decimal point becomes the positive exponent of 10.

Example

$\underbrace{18,930,000}=1.893\times {10}^7$

To write a number less than 1 in scientific notation, move the decimal point just to the right of the first nonzero number. Use the number of places you moved the decimal point as the negative exponent of 10.

Example

$0.0027=\genfrac{}{}{0.1ex}{}{2.7}{10\times 10\times 10}=2.7\times {10}^{-3}$

When you convert a number to scientific notation, remember that you are not changing the value of the number. You are only changing the way that it is written.

Examples

$500,000 = 5 \times {10}^5$

$0.000 000 042 = 4.2 \times {10}^{-8}$

$0.030 06 = 3.006 \times {10}^{-2}$

$285.2 = 2.852 \times {10}^2$

$0.0002 = 2 \times {10}^{-4}$

$83,700,000 = 8.37 \times {10}^7$

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