What Are Powers of Ten?

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The powers of 10 form a set of mathematical notations that allow you to express any number as a product of multiples of 10. Noting numbers in the powers of 10 is a useful way for engineers, mathematicians and students alike to write down very large numbers (or small numbers) instead of having to write a lot of zeros in a row. For example, 5,000 equals 5 multiplied by 1,000, or using the powers of 10 notation, you can say 5,000 equals 5 multiplied by 10 to the power of 3.

Scientific Notation

Also known as "standard form," scientific notation was given its name because it was first employed by scientists to represent very large and very small numbers. The "power" that 10 is multiplied by is also known as the exponent. These can be found in positive forms representing multiplication and negative forms representing division.

What Does a Power of 10 Equal?

The notational index of 10 tells you how many places the decimal point should move to the right. Consider what is 1.35 multiplied by 10 to the fourth power, or 1.35 x 10^4. You can calculate it as 1.35 x (10 x 10 x 10 x 10), or 1.35 x 10,000, which equals 13,500. If you were to move the decimal place in 1.35 over by four spots, you would also create 13,500.

Negative Powers of 10

When you see a negative power of 10, it indicates how many times the number should be divided by the negative power. Consider the example 5 multiplied by 10 to the negative third power, or 5 x 10^-3. Whether you write the equation out as 5 divided by 10, divided by 10, divided by 10, or you simply move the decimal place over to the left three spaces, you will arrive at 0.005, which is the numerical result of multiplying 5 by 10 to the negative third power.

Practical Example

A practical example of the powers of 10 is the way that a light year, or the distance that light travels in the span of one year, is expressed using scientific notation rather than writing out the entire numerical representation. For scientists, it is much easier to write and work with the expression 9.461 x 10^15 meters rather than 9,461,000,000,000,000 meters.


About the Author

Peter Grant has been a professional writer since 1998 and software engineer since 1995. He has contributed to academic papers, open-source software projects and technical documentation across several industries. Grant holds a master's degree in public policy from National University.

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