A height is given as 172 cm correct to the nearest centimetre. Between which two values does the height actually lie?

171.5 < height ≤ 172.5.

The lower bound is 171.5 cm and the higher bound is 172.5 cm.

Explanation:

Base on the question the height has already been approximated to the nearest centimetre. The approximated height is given as 172 centimetre to the nearest centimetre. The two value the height can actually lie can be represented as follows

171.5 < height ≤ 172.5

The tenth value which is 5 must not go below 5 (left side decimal). it should be above 5 so that the 171 can be approximated to 172. This means the height should be greater than 171.5 but it should be less than or equal to 172.5. The height cannot be 172.6 because it will be better approximated to 173 cm. This means the value of height will be 171.6, 171.7 ... 172.5 so that it can be easily approximated to 172 cm.

The lower bound is 171.5 cm and the higher bound is 172.5 cm.