Question

For each of the following statements, change the given temperature to its corresponding equivalent in \({ }^{\circ} \mathrm{C}\) or \({ }^{\circ} \mathrm{F}\). (Round to the nearest tenth.) Notify health care provider for temperature greater than \(101.4^{\circ} \mathrm{F}\). _______ \({ }^{\circ} \mathrm{C}\)

Short answer

The equivalent temperature is \( 38.6^{\circ} \mathrm{C} \).

Step-by-step solution

Identify the Given Temperature

The given temperature that needs to be converted is \( 101.4^{\circ} \mathrm{F} \).

Recall the Conversion Formula

To convert Fahrenheit to Celsius, use the formula: \( \mathrm{C} = (\mathrm{F} - 32) \times \frac{5}{9} \).

Substitute the Given Temperature

Substitute \( 101.4 \) for \( \mathrm{F} \) in the formula: \( \mathrm{C} = (101.4 - 32) \times \frac{5}{9} \).

Perform the Subtraction

First, subtract 32 from 101.4: \( 101.4 - 32 = 69.4 \).

Multiply by the Fraction

Multiply the result by \( \frac{5}{9} \): \( 69.4 \times \frac{5}{9} \).

Calculate the Result

Divide 69.4 by 9 and then multiply by 5: \( 69.4 \div 9 \approx 7.7111 \) and \( 7.7111 \times 5 \approx 38.5556 \).

Round the Result

Round \( 38.5556 \) to the nearest tenth to get \( 38.6 \).

Key concepts

Fahrenheit to Celsius

When you need to convert temperatures from Fahrenheit to Celsius, it's important to understand what these units measure. Fahrenheit and Celsius are two scales used for temperature measurement:

• Fahrenheit, abbreviated as °F, is primarily used in the United States.
• Celsius, abbreviated as °C, is used worldwide and is the standard for scientific work.

Changing from Fahrenheit to Celsius can help compare temperatures in different regions or scientific contexts. Knowing how to do this efficiently can be essential in fields like healthcare or science, where temperature plays a crucial role. In our exercise, converting a temperature of 101.4°F is necessary to ascertain its equivalent in degrees Celsius.

Conversion Formula

The foundation of converting between Fahrenheit and Celsius is the conversion formula. Formulas are like recipes in math, offering a methodical way to transform one measurement into another. For Fahrenheit to Celsius conversion, remember this simple formula: \[ C = (F - 32) \times \frac{5}{9} \]Here's how each part of the formula works:

• Subtract 32 from the Fahrenheit temperature. This accounts for the fact that the two scales have different starting points.
• The result is then multiplied by the fraction \(\frac{5}{9}\). This adjusts for the different size of units. Each degree Celsius covers more temperature change than a degree Fahrenheit because there are fewer of them between freezing and boiling of water (100°C vs. 180°F).

Using this formula ensures you accurately convert temperatures for use in other calculations or understanding, such as the health-related exercise given.

Rounding Numbers

After performing an arithmetic operation, especially multiplication or division, you often end up with many decimal places. In practical scenarios, you may need to round numbers to the nearest tenth for ease of understanding or to fit given instructions. Rounding involves looking at the first digit after your desired decimal point:

• If the digit is 0 to 4, keep the target digit the same.
• If it's 5 to 9, round up by one.

In the exercise, the temperature 38.5556°C is converted from 101.4°F. By rounding to the nearest tenth, it becomes 38.6°C. This simplification helps provide a clear and quick understanding, especially useful in settings where specific thresholds are monitored. Rounding makes complex numbers manageable and easy to communicate, especially important in high-stakes environments like healthcare.