To solve this problem, we need to consider the conversion of angles from degrees to different units. Specifically:
1. Convert 1 degree to radians
2. Convert 1 degree to gradians (sometimes called 'gons' or 'grads')
### Step-by-Step Solution:
1. Converting Degrees to Radians:
Radians are the Standard International (SI) unit for measuring angles. To convert degrees to radians, we use the fact that [tex]\(\pi\)[/tex] radians = 180 degrees.
[tex]\[ \text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
For 1 degree:
[tex]\[ \text{Radians} = 1 \times \left( \frac{\pi}{180} \right) \approx 0.017453292519943295 \][/tex]
2. Converting Degrees to Gradians:
Gradians are another unit of angular measure where 200 gradians are equivalent to 180 degrees.
[tex]\[ \text{Gradians} = \text{Degrees} \times \left( \frac{200}{180} \right) \][/tex]
For 1 degree:
[tex]\[ \text{Gradians} = 1 \times \left( \frac{200}{180} \right) = 1.1111111111111112 \][/tex]
### Conclusion:
- 1 degree is approximately 0.017453292519943295 radians.
- 1 degree is exactly 1.1111111111111112 gradians.
Therefore, the correct answer based on the conversions provided is:
- Option (d) [200] c is the closest to gradian conversion considering the information given.
- If we had to match it explicitly to the '(200) c,' it seems to be an error, but using provided results, '200' can be inferred as gradian.
Given the options, none of them point exactly to the numerically accurate conversion. So, if we must choose the closest understanding from the problem statement and options:
1 degree in gradians would be correct for option (d).
