The Rankine temperature scale $\left({ }^{\circ} \mathrm{R}\right)$ is an engineering temperature scale with $0.00^{\circ} \mathrm{R}$ at absolute zero and the same degree size as the Fahrenheit scale. Convert $186^{\circ} \mathrm{R}$ to $\mathrm{K}$ :

Step 1 ：The Rankine temperature scale (°R) is an engineering temperature scale with 0.00°R at absolute zero and the same degree size as the Fahrenheit scale. We are given a temperature of 186°R and we need to convert this to Kelvin (K).

Step 2 ：The Rankine scale is related to the Fahrenheit scale, but starts at absolute zero (like the Kelvin scale). The conversion from Rankine to Fahrenheit is given by the formula: \(F = R - 459.67\)

Step 3 ：Since we want to convert to Kelvin, we need to convert the Fahrenheit temperature to Kelvin. The conversion from Fahrenheit to Kelvin is given by the formula: \(K = (F + 459.67) * 5/9\)

Step 4 ：We can combine these two formulas to get a direct conversion from Rankine to Kelvin: \(K = R * 5/9\)

Step 5 ：So, to convert 186°R to Kelvin, we just need to multiply 186 by 5/9.

Step 6 ：Let's calculate: \(R = 186\)

Step 7 ：\(K = 186 * 5/9 = 103.33\)

Step 8 ：Final Answer: The temperature in Kelvin is \(\boxed{103.33}\)