Succeed with maths: part 2
Succeed with maths: part 2

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

2.3 Zero as a power?

The easiest way to investigate whether a number raised to the power of zero means anything mathematically, is to look at an example.

Here, start with 10 cubed division 10 cubed. Using the rules from the last section about dividing numbers with the same base number this gives us:

equation sequence 10 cubed division 10 cubed equals 10 super open three minus three close equals 10 super zero.

So, 10 cubed division 10 cubed is the same as 10 super zero

However, another way of looking at 10 cubed division 10 cubed is by writing this as a fraction and then simplifying it.

This gives:

equation sequence 10 cubed division 10 cubed equals 10 cubed divided by 10 cubed equals one

But equation left hand side 10 cubed division 10 cubed equals right hand side 10 super zero, this means that:

10 super zero equals one

So, although 100, that is ‘10 multiplied by itself zero times’ does not make any practical sense, mathematically this has the value of 1. You can use a similar argument to show that any number to the power zero has a value of 1. For example,

two super zero equals one comma 3.25 super zero equals one comma and open negative six close super zero equals one.

You could check these on your calculator now if you would like to confirm this is correct.

Remembering this rule will be very useful if you continue your study of maths, science or technology based subjects, so it is not just an interesting diversion!

Now let’s get back to scientific notation and how to show small numbers in this format. The first thing to do is though is to look at negative powers, or exponents, in the next section.

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371