Question

part 1 of 6
96.5 °f, the temperature on a hot summer day = 35.8 °c
part 2 of 6
10.4 °f, the temperature on a cold winter day = -12.0 °c
part 3 of 6
a 102.8 °f fever = 39.33 °c
part 4 of 6
a furnace operating at 2023.5 °f = 1105.3 °c
part 5 of 6
-273.15 °c (theoretically the lowest attainable temperature) = -459.67 °f
part 6 of 6
-27.84 °c = -18.11 °f

Explanation:

Step1: Recall temperature - conversion formula

The formula to convert Fahrenheit ($F$) to Celsius ($C$) is $C=\frac{5}{9}(F - 32)$, and to convert Celsius to Fahrenheit is $F=\frac{9}{5}C+32$.

Step2: Part 1 conversion

For $F = 96.5^{\circ}F$, $C=\frac{5}{9}(96.5 - 32)=\frac{5}{9}\times64.5\approx35.8^{\circ}C$.

Step3: Part 2 conversion

For $F = 10.4^{\circ}F$, $C=\frac{5}{9}(10.4 - 32)=\frac{5}{9}\times(- 21.6)=-12.0^{\circ}C$.

Step4: Part 3 conversion

For $F = 102.8^{\circ}F$, $C=\frac{5}{9}(102.8 - 32)=\frac{5}{9}\times70.8\approx39.33^{\circ}C$.

Step5: Part 4 conversion

For $F = 2023.5^{\circ}F$, $C=\frac{5}{9}(2023.5 - 32)=\frac{5}{9}\times1991.5\approx1105.3^{\circ}C$.

Step6: Part 5 conversion

For $C=-273.15^{\circ}C$, $F=\frac{9}{5}\times(-273.15)+32=-491.67 + 32=-459.67^{\circ}F$.

Step7: Part 6 conversion

For $C=-27.84^{\circ}C$, $F=\frac{9}{5}\times(-27.84)+32=-50.112+32=-18.11^{\circ}F$.

Answer:

Part 1: $35.8^{\circ}C$
Part 2: $-12.0^{\circ}C$
Part 3: $39.33^{\circ}C$
Part 4: $1105.3^{\circ}C$
Part 5: $-459.67^{\circ}F$
Part 6: $-18.11^{\circ}F$