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The fraction 355/113 is a famous value for π, far better than 22/7…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The fraction $\dfrac{355}{113}$ is a famous value for $\pi$ , far better than $\dfrac{22}{7}$ . Find it to seven decimal places and compare it with $\pi = 3.14159265\ldots$ . How big is the difference? Can any fraction be exactly $\pi$ ?

Need a reminder? The key ideaShow

An irrational number cannot be written as $\dfrac{p}{q}$ . Its decimal never ends and never repeats. $\sqrt{n}$ is irrational when the whole number $n$ is not a perfect square. Rational and irrational numbers together make the real numbers.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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