The coldest temperature ever measured in the United States was \(-80^{\circ} \mathrm{F}\) on January 23,1971 , in Prospect Creek, Alaska. Convert that temperature to degrees Celsius and Kelvin. (Assume that \(-80^{\circ} \mathrm{F}\) is accurate to two significant figures.)

Understanding how to convert temperature from Fahrenheit to Celsius is essential for scientific studies and everyday life, especially when traveling or studying weather patterns. The conversion is done using the formula:

\( C = \frac{5}{9}(F - 32) \)

To use this formula, subtract 32 from the Fahrenheit temperature and then multiply the result by \( \frac{5}{9} \). For example, with the coldest temperature ever measured in the United States being \(-80^{circ} \mathrm{F}\), we first calculate the intermediate step: \(-80 - 32 = -112\). Then, apply the multiplier: \( \frac{5}{9}(-112) \), resulting in the temperature in Celsius. When executing these steps, it's important to be aware of the significant figures and rounding rules to ensure the precision of the result aligns with the data provided.

Converting Celsius to Kelvin is a straightforward process involving a simple addition. The Kelvin scale is an absolute temperature scale, used predominantly in the scientific community. The conversion formula is:

\( K = C + 273.15 \)

In this formula, 'C' represents the temperature in Celsius, and 273.15 is the numerical value that defines the difference between the zero points of the Celsius and Kelvin scales. Taking our previously converted \(-62.222\ldots \) degrees Celsius, it would be converted into Kelvin by simply adding 273.15 to get \( -62.222 + 273.15 \) Kelvin. The precision of the Celsius measurement directly affects the final Kelvin result, highlighting the importance of significant figures in this step.

The concept of significant figures is a fundamental aspect of precision in scientific measurements. They represent all the known digits plus one estimated digit in a measurement, providing a sense of the precision of the measurement and the instruments used to obtain it.

To work with significant figures, follow these guidelines:

• Non-zero digits are always significant.
• Any zeros between significant digits are also significant.
• Leading zeros are not significant as they serve only to position the decimal point.
• Trailing zeros in a number containing a decimal point are significant.

When we converted the historically low temperature of \(-80^{circ} \mathrm{F}\) to Celsius, we treated it as having two significant figures, as this depicts the measurement's accuracy. Later, while converting from Celsius to Kelvin, the constants we used (273.15) dictated the number of significant figures in our final answer, which is technically limited by the precision of our initial measurement. To properly convey measurements and calculations in scientific work, mastering the use of significant figures is crucial.