Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(0^{\circ} \mathrm{F}=\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

0°F is approximately -17.8°C.

Step-by-step solution

Understand the Conversion Formula

To convert from 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.

Input the Fahrenheit Temperature

Substitute \( F = 0 \) into the conversion formula. The equation becomes: \( C = \frac{5}{9}(0 - 32) \).

Calculate the Difference

First, calculate the difference inside the parentheses: \( 0 - 32 = -32 \). The formula now reads \( C = \frac{5}{9}(-32) \).

Multiply by the Conversion Factor

Calculate \( \frac{5}{9} \times (-32) \). First, divide \(-32\) by \( 9 \) to get approximately \(-3.56\). Then, multiply by \(5\) to get \(-17.78\).

Round the Result

Round \(-17.78\) to the nearest tenth. This gives \( C \approx -17.8 \).

Key concepts

Fahrenheit to Celsius

Temperature is a fundamental concept in science and daily life, and understanding how to convert from one scale to another is essential. In the United States, temperatures are often given in Fahrenheit, whereas Celsius is used in many other parts of the world.

To convert a temperature from Fahrenheit to Celsius, it's important to understand what each scale represents:

• Fahrenheit: This scale is named after Daniel Gabriel Fahrenheit. In this scale, water freezes at 32 degrees and boils at 212 degrees.
• Celsius: Also called centigrade, this scale sets the freezing point of water at 0 degrees and boiling at 100 degrees, making it logical and straightforward.

Grasping the relationship between these two units allows us to convert seamlessly.

Conversion Formula

When converting Fahrenheit to Celsius, we rely on a specific formula. This formula bridges the gap between the two temperature scales.

The formula to convert Fahrenheit (F) to Celsius (C) is:\[ C = \frac{5}{9}(F - 32) \]

• Step 1: Subtract 32 from the given Fahrenheit (Fahrenheit scale's freezing point of water).
• Step 2: Multiply the result from step 1 by \(\frac{5}{9}\). This fraction stems from the ratio of the intervals in the Celsius and Fahrenheit scales.

Following this formula allows you to quickly and accurately transition between Fahrenheit and Celsius. It's essential to master this formula for both academic and practical applications.

Rounding Decimals

Once we have used the formula to convert Fahrenheit to Celsius, the result may not always come out as a neat whole number. Often, it will be a decimal which needs rounding. This step ensures the temperature is practical for everyday use.

Here’s how to round decimals:

• Identify the target decimal place: Typically, we round to the nearest tenth.
• Check the next smallest place value: If this number is 5 or greater, increase the target place by 1. If not, keep the target number the same.

For the temperature conversion exercise, \(-17.78\) rounded to the nearest tenth becomes \(-17.8\). This skill is crucial not just in temperature conversion, but in all forms of numerical data analysis.

Step-by-step Calculation

Performing temperature conversion accurately involves a clear understanding of each mathematical step involved. Following a structured sequence can help avoid mistakes and improve mathematical thinking.

To convert 0°F to Celsius, let’s break it down:

• Substitute: Replace F with 0 in the formula: \( C = \frac{5}{9}(F - 32) \).
• Calculate the Difference: \( 0 - 32 = -32 \). The expression becomes \( C = \frac{5}{9}(-32) \).
• Multiply by the Fraction: Compute \( \frac{5}{9} \times (-32) \): first divide -32 by 9 (approx. -3.56), then multiply by 5 to yield -17.78.
• Round: Finally, round -17.78 to the nearest tenth, resulting in -17.8°C.

This methodical approach ensures the conversion is calculated properly, allowing for a high degree of accuracy.