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.) Do not expose medication to temperatures greater than \(88^{\circ} \mathrm{F}\). _______ \({ }^{\circ} \mathrm{C}\)

Short answer

31.1°C

Step-by-step solution

Identify the Formula

To convert Fahrenheit to Celsius, use the formula: \[ C = \frac{5}{9} (F - 32) \] where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

Substitute the Value

In the given problem, the temperature in Fahrenheit is \( 88^{\circ} \). Substitute \( F = 88 \) into the formula:\[ C = \frac{5}{9} (88 - 32) \]

Perform the Calculation

Subtract \( 32 \) from \( 88 \):\[ 88 - 32 = 56 \]Now, multiply \( 56 \) by \( \frac{5}{9} \):\[ C = \frac{5}{9} \times 56 = \frac{280}{9} \]

Simplify and Round

Divide \( 280 \) by \( 9 \):\[ \frac{280}{9} = 31.1111... \]Round to the nearest tenth to get \( 31.1 \).

Key concepts

Fahrenheit to Celsius Conversion Made Easy

Temperature conversion is common in math and science. One of the most frequent conversions is from Fahrenheit to Celsius. Here's a straightforward way to understand it.

The formula for this conversion is simple: \[ C = \frac{5}{9} (F - 32) \] where:

• \( C \) stands for degrees Celsius.
• \( F \) is degrees Fahrenheit.

This formula subtracts 32 from the Fahrenheit value to adjust for the starting point differences between the two scales. This first step aligns the scales at their freezing points (32°F is 0°C).

Next, multiply the result by \( \frac{5}{9} \). This fraction accounts for the different sizes of one degree on each scale. One Celsius degree is larger than one Fahrenheit degree. Using \( \frac{5}{9} \) adjusts for this difference. The calculation shows how many Celsius degrees correspond to a change in Fahrenheit degrees.

Using this formula, like in the example of converting 88°F, helps you find the temperature in Celsius efficiently.

Rounding Temperatures Accurately

Rounding is essential in temperature conversion, especially for precise tasks like scientific experiments or medicine. After calculating the Celsius equivalent, you'll likely get a number with several decimal places. Knowing how to round these numbers is crucial.

Start by looking at the decimal number. Let's say it is 31.1111. To round to the nearest tenth, focus on the first decimal place.

• If this digit is 5 or higher, round up.
• If it's 4 or lower, round down.

In the example of 31.1111, the first decimal is 1. Since it's less than 5, you simply keep the 31 and round down, obtaining 31.1.

This rule ensures that temperatures are accurate and easy to interpret, especially when precise measurements are required. By rounding properly, you maintain the integrity of the information while presenting it in an understandable format.

Applying Mathematical Formulas Correctly

When performing tasks such as temperature conversion, applying a mathematical formula accurately is critical to success. It's not just about knowing the formula but about applying it in the right order.

Start with clear identification of the values you are working with. Identify \( F \), the given Fahrenheit temperature, or the initial measurement, and clearly plan your formula steps.

• Subtract 32 from the Fahrenheit value. This step adjusts the measurement to the Celsius scale start point.
• Multiply the result by \( \frac{5}{9} \) for converting the changed Fahrenheit degrees to Celsius degrees.

Follow each step carefully to avoid common mistakes like skipping operations or incorrect arithmetic, which can lead to inaccurate results.

Double-check that each arithmetic operation is done accurately. These steps convert a real-world problem into a manageable arithmetic task. Remember that precision in using formulas ensures that your solutions are both correct and reliable. This process not only simplifies complex problems but enhances your overall problem-solving skills.