Powers of 10
(KS2, Year 4)

A power of 10 is 10 raised to a exponent. For example, 10² is a power of 10.

The small 2 written beside the 10 means it is raised to an exponent of 2. This means 10 is multiplied by itself 2 times.

Understanding a Power of 10

A power is the product of multiplying a number by itself. A power of 10 is 10 multiplied by itself. The exponent written beside the 10 tells you how many times 10 is multiplied by itself.

• When the exponent is 2, 10 is multiplied by itself 2 times. The product is 100. There are 2 0s after the 1.
• When the exponent is 3, 10 is multiplied by itself 3 times The product is 1,000. There are 3 0s after the 1.

Why Are Powers of 10 Useful?

Powers of 10 are useful because they allow us to write very large (or very small) numbers in an easy way. If we wanted to write one million in full, we would have to write a lot of numbers down: Using powers of 10, we can write it much more easily as a power of 10. There are 6 0s after the 1, so the exponent is 6: This is useful for scientists and engineers when they write large quantities down. For example, the speed of light is approximately 300 million metres per second: A scientist or engineer would write this using powers of 10: There are 8 0s. The 0s come after a 3, so we need to multiply the power of 10 by 3. This way of writing numbers is called scientific notation. scientific notation

The Parts of a Power of 10

A power of 10 has the same parts as any power. It consists of a base and an exponent.

• The base is the number that is multiplying itself. In a power of 10, the base is always 10.
• The exponent tells you how many times the base is multiplying by itself. It is any whole number (any integer). It can be positive or negative.

Positive and Negative Exponents

All the examples of powers of 10 we have seen so far have positive exponents.

This power of 10 has an exponent of positive 2. If you start with 1 and move the decimal point 2 places to the right, you get 100. This is why there are 2 0s after the 1.

A power of 10 can also have a negative exponent.

This power of 10 has an exponent of negative 2. If you start with 1 and move the decimal point 2 places to the left, you get 0.02. This is why there are 2 0s before the 1.

Note

Useful Powers of 10

Here are two useful powers of 10:

Googols and Googolplexes

A googol is 10¹⁰⁰: that is 1 followed by 100 0s. It is a bigger number than the number of particles in the universe (about 10⁸⁰). The googol gave its name to a famous search engine company. A googleplex is 10 with an exponent of a googol.