Question

If temperature of an object is \(140^{\circ} \mathrm{F}\) then its temperature in centigrade is (A) \(105^{\circ} \mathrm{C}\) (B) \(32^{\circ} \mathrm{C}\) (C) \(140^{\circ} \mathrm{C}\) (D) \(60^{\circ} \mathrm{C}\)

Short answer

The correct answer is (D) \(60^{\circ} \mathrm{C}\), which is obtained by using the Fahrenheit to Celsius conversion formula \(C = (F - 32) × \frac{5}{9}\) and plugging in the given temperature of \(140^{\circ} \mathrm{F}\).

Step-by-step solution

Write down the given temperature in Fahrenheit

We are given the temperature of an object as \(140^{\circ} \mathrm{F}\).

Use the conversion formula to convert the temperature into Celsius

The formula for converting Fahrenheit to Celsius is: \[C = (F - 32) × \frac{5}{9}\] Now, plug in the given Fahrenheit temperature (F = 140) into the formula: \[C = (140 - 32) × \frac{5}{9}\]

Calculate the Celsius temperature

Perform the calculations inside the parentheses first, and then multiply by the fraction: \[C = (108) × \frac{5}{9}\] Divide 108 by 9: \[C = 12 × 5\] Now, multiply 12 by 5: \[C = 60\] Thus, the temperature in Celsius is \(60^{\circ} \mathrm{C}\). The correct answer is (D) \(60^{\circ} \mathrm{C}\).

Key concepts

Fahrenheit to Celsius Conversion

Converting from Fahrenheit to Celsius is a fundamental concept in understanding temperature differences across different regions and for scientific measurements. To convert a temperature reading from Fahrenheit to Celsius, you can use the formula:

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

This formula helps to adjust for the differing starting points and degrees of scale between the two units.
The quantifier \(-32\) corrects the Fahrenheit scale to align it with the Celsius starting point. Meanwhile, the multiplication by \(\frac{5}{9}\) ensures that the degrees are in harmony in terms of size, as every degree Celsius equals 1.8 degrees Fahrenheit.
Employing this formula ensures precise temperature readings that can be applied in global scientific contexts.

Temperature Scales

Temperature scales allow us to measure heat and coldness, fundamental aspects of the physical world. The Fahrenheit and Celsius scales are two such systems, with unique characteristics.
The Fahrenheit scale is primarily used in the United States and a few other countries. In this scale, water freezes at \(32^{\circ}\) and boils at \(212^{\circ}\).
On the other hand, the Celsius scale is commonly used worldwide for scientific measurements, due to its straightforward design where water freezes at \(0^{\circ}\) and boils at \(100^{\circ}\). This makes it a preferred scale in scientific contexts, owing to its simplicity and ease of use.

• Each degree in Celsius is larger than each degree in Fahrenheit.
• It's common in countries that use the metric system.

Understanding these scales' principles is crucial for accurately converting and comparing temperature measures.

Mathematical Calculation Steps

Performing the conversion between Fahrenheit and Celsius is an exercise in basic algebra and arithmetic, highlighting the importance of order in mathematical operations.
During the conversion, the sequence of calculations is key:

• First, subtract 32 from the Fahrenheit number. This recalibrates the measurement from its unique scale.
• Next, multiply the resultant value by \(\frac{5}{9}\). This fraction adjusts the discrepancy in size between the Fahrenheit and Celsius degrees.
• For instance, converting \(140^{\circ} \mathrm{F}\) involves these steps: \((140 - 32) \times \frac{5}{9}\).
• Perform the arithmetic: \(140 - 32 = 108\); then \(108 \times \frac{5}{9} = 60\).

This structured procedure ensures that our conversion is error-free and consistent. Such calculations are essential for anyone working in fields that require precise temperature data.