Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(50^{\circ} \mathrm{F}=\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

\(50^{\circ} \mathrm{F} = 10^{\circ} \mathrm{C}\).

Step-by-step solution

Write Down the Formula

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

Substitute the Given Value

Let's substitute the given Fahrenheit temperature into the formula. We have:\[°C = \frac{5}{9} \times (50 - 32)\]

Calculate the Difference

First, calculate the difference between 50 and 32:\[50 - 32 = 18\]

Multiply by Fraction

Next, we multiply the result by \(\frac{5}{9}\):\[°C = \frac{5}{9} \times 18\]

Simplify the Multiplication

Calculate the multiplication:\[°C = 10\]

Round the Result to the Nearest Tenth

In this case, the result (10) already is a whole number, so it remains the same when rounded to the nearest tenth.

Key concepts

Fahrenheit to Celsius Conversion

Understanding how to convert from Fahrenheit to Celsius is a valuable skill, especially for science or travel-related applications. The Fahrenheit scale, used primarily in the United States, differs from the Celsius scale, prevalent in most other countries.
This difference is due to how each scale defines temperature measurements.

• On the Fahrenheit scale, water freezes at 32 degrees and boils at 212 degrees.
• In Celsius, water freezes at 0 degrees and boils at 100 degrees.

The key to converting between these two scales is a specific mathematical relationship that allows temperature to be recalculated without direct tools, using only mathematical computation. Understanding and applying this will enable you to work efficiently between Fahrenheit and Celsius.

Mathematical Formula

The mathematical formula needed for converting temperatures from Fahrenheit to Celsius is straightforward yet fundamental. The formula is:
\[°C = \frac{5}{9} \times (°F - 32)\]
- This formula originates from the relative sizes of the degree units on each scale, where the Celsius scale has 100 units between the freezing and boiling points of water, while Fahrenheit has 180. The subtraction of 32 accounts for the offset in the starting point of freezing water in both scales. The fraction \(\frac{5}{9}\) represents the ratio between the size of one degree Fahrenheit to one degree Celsius (since 180/100 simplifies to 9/5, its reciprocal 5/9 is used in conversion from Fahrenheit to Celsius).
Understanding this relationship will enable you to apply the formula confidently and accurately adapt temperatures between the two units.

Step-by-Step Calculation

Carrying out the conversion requires a step-by-step approach that ensures the calculation is accurate. Let’s walk through a conversion using the example provided:
1. **Write the Formula:** Start by writing down the formula:
\[°C = \frac{5}{9} \times (°F - 32)\] 2. **Substitute the Given Value:** Insert the Fahrenheit temperature you need to convert into the formula:
\[°C = \frac{5}{9} \times (50 - 32)\] 3. **Calculate the Difference:** Evaluate the expression inside the parenthesis first:
\[50 - 32 = 18\] 4. **Multiply by Fraction:** Multiply the obtained difference by \(\frac{5}{9}\) to complete the conversion:
\[°C = \frac{5}{9} \times 18\] 5. **Simplify the Multiplication:** Simplify to get the Celsius value:
\[°C = 10\]

By understanding and following these steps, you ensure no part of the process is skipped, which is crucial for getting the correct answer every time.

Rounding Numbers

Rounding numbers is a mathematical technique crucial for approximating values without overly affecting the precision needed for meaningful results.
After calculating the conversion, you often may need to round to a certain decimal place.
In our case, rounding to the nearest tenth involves checking the digit in the hundredths place (the first digit beyond your desired precision):
- If the hundredths digit is 5 or greater, increase the tenths digit by one. - If it is less than 5, keep the tenths digit as is.
Let's apply this to our example with a result of 10. Since there are no additional decimal places beyond the tenth in this case, no actual rounding is necessary. For other numbers that aren't whole, this simple yet effective approach helps keep answers neat and standardized, especially when significant precision isn't crucial, such as in everyday temperature readings.