Question

Provide an expansion of π to 5 decimal places. Confirm your understanding that π can be computed to an indefinite precision and that an expansion to 5 decimal places is only an approximation for the real value of π.

Answer 1

π = 3.14286 to 5dp

Explanation:

π as a value is
`(22)/(7)`. Expresssing
`(22)/(7)` as decimal will give;

π =
`(22)/(7)` = 3.142857 142857 142857 1...

It can be seen that the values after the decimal point goes indefinitely by continually imputing the value 142857 based on the segregation. Therefore an expansion to 5dp is the only approximate value for π since the remaining values are mere repetition.

Converting to 5 decimal places means having just 5 values after the decimal point as shown;

`\pi = (22)/(7) = 3.14286`

The last value is rounded up to 6 because the succeeding value is 7(which is more than 5). In this case 1 will be added to the fifth place value in the figure rounding it up to 6.