Answer :
We know that when a measurement is given as 100 metres correct to the nearest metre, the actual length is rounded to 100. This means the true length [tex]$x$[/tex] satisfies:
[tex]$$
100 - 0.5 \leq x < 100 + 0.5
$$[/tex]
Simplifying the inequality, we get:
[tex]$$
99.5 \leq x < 100.5
$$[/tex]
Thus, the error interval for the length of the rugby pitch is:
[tex]$$
\boxed{99.5\text{ m} \leq \text{length} < 100.5\text{ m}}
$$[/tex]
[tex]$$
100 - 0.5 \leq x < 100 + 0.5
$$[/tex]
Simplifying the inequality, we get:
[tex]$$
99.5 \leq x < 100.5
$$[/tex]
Thus, the error interval for the length of the rugby pitch is:
[tex]$$
\boxed{99.5\text{ m} \leq \text{length} < 100.5\text{ m}}
$$[/tex]
