Conversion between decimeters and centimeters:
To understand why the correct answer is option 'A', let's first review the conversion between decimeters and centimeters.

Definition:
Decimeter (dm) and centimeter (cm) are both units of length in the metric system.

- 1 decimeter (dm) is equal to 10 centimeters (cm).

In other words, 1 decimeter is made up of 10 centimeters.

Explanation of the correct answer:
Now, let's look at the options given in the question and determine which one is the correct conversion from decimeters to centimeters.

a) 10
b) 50
c) 100
d) 1000

To convert decimeters to centimeters, we multiply the number of decimeters by 10. So, the correct conversion is option 'A' which states that 1 decimeter has 10 centimeters.

Explanation of other options:
b) 50: This option is incorrect because it does not follow the correct conversion factor of multiplying by 10. Multiplying 1 decimeter by 50 would result in 50 centimeters, which is not accurate.

c) 100: This option is also incorrect. Multiplying 1 decimeter by 100 would result in 100 centimeters, which is not accurate according to the correct conversion factor.

d) 1000: This option is incorrect as well. Multiplying 1 decimeter by 1000 would result in 1000 centimeters, which is not the accurate conversion.

Conclusion:
The correct answer is option 'A' because 1 decimeter is equal to 10 centimeters. This conversion factor is a fundamental concept in the metric system and is used to convert between these two units of length.

10