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Difficulty: MediumTemperature Scales

An industrial oven used for curing aerospace composites is set to a precise temperature of 680∘F680^\circ\text{F}. To program a secondary backup sensor that operates exclusively on the Celsius scale, what numerical value must the technician enter?

Answer: 360 ^\circ\text{C}

Answer

360
The correct equivalent temperature is found by first subtracting 32 from the Fahrenheit value to adjust for the different zero points, resulting in 648648. Multiplying this difference by 59\frac{5}{9} accounts for the different degree increments between the scales, producing an exact value of 360∘C360^\circ\text{C}.

Step-by-Step Solution

1
Set up the conversion equation.
C=59(680−32)C = \frac{5}{9}(680 - 32)
This is the standard formula to convert degrees Fahrenheit into degrees Celsius.
2
Perform the subtraction inside the parentheses.
680−32=648680 - 32 = 648
According to the order of operations, the offset between the two temperature scales must be removed first.
3
Multiply the difference by the fraction 59\frac{5}{9}.
648÷9=72648 \div 9 = 72, then 72×5=36072 \times 5 = 360
Multiplying by 59\frac{5}{9} scales the Fahrenheit degree magnitude to match the Celsius degree magnitude.

Key Concept

Temperature Scale Conversion
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Topics

Temperature Scales

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