a. Convert 55∘16′30″ into radian measure.
b. Convert 10∘10′10″ into a censusimal system.

Let's solve the two parts of the question step by step.

Part (a): Convert 55°16′30″ into radian measure.
Understand the components:

55° = 55 degrees
16′ = 16 minutes (1 minute = 1/60 of a degree)
30″ = 30 seconds (1 second = 1/3600 of a degree)
Convert the degrees, minutes, and seconds into a single value in degrees:

55° is already in degrees.
Convert 16 minutes into degrees: 16′ = 16/60 degrees = 0.2667 degrees.
Convert 30 seconds into degrees: 30″ = 30/3600 degrees = 0.0083 degrees.
So, the total in degrees is: Total degrees = 55 + 0.2667 + 0.0083 = 55.275 degrees.

Convert degrees to radians: The formula to convert degrees to radians is: radians = degrees × (π / 180)

Substituting 55.275 degrees: radians = 55.275 × (π / 180) radians ≈ 55.275 × 0.0174533 radians ≈ 0.963 radians

Thus, 55°16′30″ is approximately 0.963 radians.

Part (b): Convert 10°10′10″ into a censusimal system.
Understand the components:

10° = 10 degrees
10′ = 10 minutes
10″ = 10 seconds
Convert the degrees, minutes, and seconds into a single value in decimal degrees:

10° is already in degrees.
Convert 10 minutes into a decimal fraction of a degree: 10′ = 10/60 = 0.1667 degrees.
Convert 10 seconds into a decimal fraction of a degree: 10″ = 10/3600 = 0.0028 degrees.
So, the total in decimal degrees is: Total degrees = 10 + 0.1667 + 0.0028 = 10.1695 degrees.

Convert the decimal degrees into a censusimal system (based on 100 parts for each degree): The whole number part (10) remains the same.

0.1695 degrees = 1695 centesimal minutes (since 1 decimal degree = 100 centesimal minutes).
Thus, 10°10′10″ is approximately 10° 1695 centesimal minutes in the censusimal system.

Final Answers:
a) 55°16′30″ ≈ 0.963 radians
b) 10°10′10″ ≈ 10° 1695 centesimal minutes