The height, h metres, of a boy is 1.72 m, correct to the nearest centimetre. Complete this statement about the value of h. _ < h <
The Correct Answer and Explanation is:
The correct statement is: 1.715 < h < 1.725
Explanation:
To solve this problem, we must understand what it means for a measurement to be correct to the nearest centimetre. The height given is 1.72 metres, which is equivalent to 172 centimetres since 1 metre contains 100 centimetres.
When rounding to the nearest centimetre, the actual measurement could be slightly smaller or larger but still round to 172 cm when rounded correctly. This means the true value of h could be anywhere between 171.5 cm and 172.5 cm, since any value in this range would round to 172 cm.
Now, converting these values back into metres:
- 171.5 cm is 1.715 m
- 172.5 cm is 1.725 m
Since the height was rounded to the nearest centimetre, the actual height must be strictly greater than 1.715 m and strictly less than 1.725 m. That is why the correct statement is 1.715 < h < 1.725.
Why This Matters:
Understanding rounding and precision is important in mathematics and science. Many real-world applications rely on correctly interpreting measurements, such as engineering designs, medical dosing calculations, and physics experiments. When measurements are rounded, knowing their possible range helps prevent errors in calculations and ensures accuracy.
This concept also applies to significant figures and tolerances in scientific research. For example, when measuring lengths in a lab, rounding conventions ensure consistency, but a scientist must always account for possible variations in the actual values. By mastering this principle, one can make more precise estimates and better understand numerical representations in practical scenarios.
