Find the circumference of a circle whose radius is 28 centimetres.

Step-by-step solution

1. 1

   Write the formula and decide which π to use. The circumference is

   $C=2\pi r$

   The radius $28$ is a multiple of $7$, which is precisely when the approximation $\pi\approx\tfrac{22}{7}$ is convenient: the $7$ in the denominator cancels and the arithmetic stays exact in whole numbers. (This is an approximation, chosen for convenience — not a different value of $\pi$.)

2. 2

   Substitute.

   $C=2\times\frac{22}{7}\times 28$

3. 3

   Cancel before multiplying. Since $28\div 7=4$,

   $C=2\times 22\times 4$

4. 4

   Multiply.

   $C=44\times 4=176\ \text{cm}$

   $\boxed{176\ \text{cm}}$

5. 5

   Compare with the exact value. Exactly, $C=56\pi\ \text{cm}=175.93\ \text{cm}$. The $\tfrac{22}{7}$ answer of $176$ cm is high by about $0.07$ cm — roughly $0.04\%$ — so it is fine for a school answer but should be quoted as $56\pi$ when an exact result is wanted.