Question
Two commonly used approximations of $\pi$ are $22 / 7$ and 3.14. How can you tell at a glance that these approximations cannot be exact?
Step 1
An irrational number cannot be expressed as a ratio of two integers. In mathematical terms, if a number is irrational, it cannot be expressed as $p/q$, where $p$ and $q$ are integers. Show more…
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Numbers that are sometimes used as approximations of $\pi$ are 3.14 and $3 \frac{1}{7} .$ To four decimal places, $\pi$ is 3.1416 An especially good approximation of $\pi$ is the fraction $\frac{355}{113}$. To how many decimal places does it give the correct value?
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Numbers that are sometimes used as approximations of $\pi$ are 3.14 and $3 \frac{1}{7} .$ To four decimal places, $\pi$ is 3.1416 Which approximation of $\pi$ is better: 3.14 or $3 \frac{1}{7} ?$
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