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# Powers of 10

The powers of 10 are easy to remember because we use a base 10 number system. That means that ${10}^{n}$ is always equal to "1" with n zeros after it provided that n is a positive integer. Negative powers represented by ${10}^{-n}$ are always a decimal less than 1 starting with "0." followed by $n-1$ zeros and then a 1 provided that n is a negative integer. With these two tricks, you can decipher any integer power of 10 you're likely to come across.

The powers of 10 are frequently used in scientific notation, so you should try to feel as comfortable with them as possible. It's often easier to write ${10}^{17}$ than 100,000,000,000,000,000 if you're working with huge numbers in any capacity. Without further ado, let's explore the powers of 10 and what they do.

## What are some common powers of 10?

You aren't expected to memorize all of the powers of 10, but it would help to know some frequently seen examples. The following table provides information on some of the most common powers of 10:

 ${10}^{1}=10$ ${10}^{0}=1$ ${10}^{2}=100$ ${10}^{-1}=0.1$ ${10}^{3}=1000$ ${10}^{-2}=1000$ ${10}^{4}=10000$ ${10}^{-3}=0.001$ ${10}^{5}=100000$ (one hundred thousand) ${10}^{-4}=0.0001$ (one ten-thousandth) ${10}^{6}=1000000$ (one million) ${10}^{-5}=0.00001$ (one hundred-thousandth) ${10}^{7}=10000000$ (ten million) ${10}^{-6}=0.000001$ (one millionth) ${10}^{8}=100000000$ (one hundred million) ${10}^{-7}=0.0000001$ (one ten-millionth) ${10}^{9}=1000000000$ (one billion) ${10}^{-8}=0.00000001$ (one hundred-millionth) ${10}^{8}=10000000000$ (ten billion) ${10}^{-9}=0.000000001$ (one billionth)

Did you know that different countries call big numbers by different names? For example, Americans say that ${10}^{9}$ is one billion while the British call that same number "one thousand million." Other cultures also do different things with commas. For instance, commas are placed after every two zeros instead of three after 1,000 in India. Our primer on really big and small numbers can help you better understand these differences and how they relate to the powers of 10.

## Powers of 10 practice questions

a. What number is represented by ${10}^{7}$ ?

10,000,000

b. What number is represented by ${10}^{-8}$ ?

0.00000001

c. How would you express 100,000,000,000 as a power of 10?

${10}^{11}$

d. How would you express 0.000000000001 as a power of 10?

${10}^{-12}$

e. When would you use negative powers of 10?

When there are significant digits behind a decimal point.

## Get help with the powers of 10 today with Varsity Tutors

Studying the powers of 10 may feel like an isolated topic in the broader study of mathematics, but it serves as an introduction to exponents and working with very large and small numbers. If your student is having trouble with the powers of 10 now, the issue may get worse if it isn't addressed. That's why it's so important to understand math concepts as they're taught. Fortunately, a private math tutor can help students of all ages and ability levels feel more comfortable in the classroom as they pursue their educational goals. The Educational Directors at Varsity Tutors can explain more about the benefits of tutoring and sign your student up to start sessions with a math tutor, but we can't start until you reach out. Get in touch today!

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