Let's solve each problem step by step using the formulas provided in the worksheet.
---
Formulas:
-
Fahrenheit to Celsius:
$$
C^\circ = \frac{5}{9}(F^\circ - 32)
$$
-
Celsius to Fahrenheit:
$$
F^\circ = \frac{9}{5}C^\circ + 32
$$
-
Celsius to Kelvin:
$$
K^\circ = C^\circ + 273.15
$$
-
Kelvin to Celsius:
$$
C^\circ = K^\circ - 273.15
$$
---
##
Part 1: Convert the following to Fahrenheit
Use:
$$
F^\circ = \frac{9}{5}C^\circ + 32
$$
1) $10^\circ C$
$$
F = \frac{9}{5}(10) + 32 = 18 + 32 = 50^\circ F
$$
2) $30^\circ C$
$$
F = \frac{9}{5}(30) + 32 = 54 + 32 = 86^\circ F
$$
3) $40^\circ C$
$$
F = \frac{9}{5}(40) + 32 = 72 + 32 = 104^\circ F
$$
4) $37^\circ C$
$$
F = \frac{9}{5}(37) + 32 = 66.6 + 32 = 98.6^\circ F
$$
5) $0^\circ C$
$$
F = \frac{9}{5}(0) + 32 = 0 + 32 = 32^\circ F
$$
---
##
Part 2: Convert the following to Celsius
Use:
$$
C^\circ = \frac{5}{9}(F^\circ - 32)
$$
6) $32^\circ F$
$$
C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0^\circ C
$$
7) $45^\circ F$
$$
C = \frac{5}{9}(45 - 32) = \frac{5}{9}(13) \approx 7.22^\circ C
$$
8) $70^\circ F$
$$
C = \frac{5}{9}(70 - 32) = \frac{5}{9}(38) \approx 21.11^\circ C
$$
9) $80^\circ F$
$$
C = \frac{5}{9}(80 - 32) = \frac{5}{9}(48) \approx 26.67^\circ C
$$
10) $90^\circ F$
$$
C = \frac{5}{9}(90 - 32) = \frac{5}{9}(58) \approx 32.22^\circ C
$$
---
##
Part 3: Convert the following to Kelvin
Use:
$$
K^\circ = C^\circ + 273.15
$$
11) $212^\circ F$ → First convert to Celsius, then to Kelvin
$$
C = \frac{5}{9}(212 - 32) = \frac{5}{9}(180) = 100^\circ C
\Rightarrow K = 100 + 273.15 = 373.15\,K
$$
12) $0^\circ C$
$$
K = 0 + 273.15 = 273.15\,K
$$
13) $-50^\circ C$
$$
K = -50 + 273.15 = 223.15\,K
$$
14) $90^\circ C$
$$
K = 90 + 273.15 = 363.15\,K
$$
15) $-20^\circ C$
$$
K = -20 + 273.15 = 253.15\,K
$$
---
##
Part 4: Convert the following to Celsius
Use:
$$
C^\circ = K^\circ - 273.15
$$
16) $100\,K$
$$
C = 100 - 273.15 = -173.15^\circ C
$$
17) $200\,K$
$$
C = 200 - 273.15 = -73.15^\circ C
$$
18) $273\,K$
$$
C = 273 - 273.15 = -0.15^\circ C \quad (\text{approximately } 0^\circ C)
$$
19) $350\,K$
$$
C = 350 - 273.15 = 76.85^\circ C
$$
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✔ Final Answers:
#### Convert to Fahrenheit:
1) $50^\circ F$
2) $86^\circ F$
3) $104^\circ F$
4) $98.6^\circ F$
5) $32^\circ F$
#### Convert to Celsius:
6) $0^\circ C$
7) $7.22^\circ C$
8) $21.11^\circ C$
9) $26.67^\circ C$
10) $32.22^\circ C$
#### Convert to Kelvin:
11) $373.15\,K$
12) $273.15\,K$
13) $223.15\,K$
14) $363.15\,K$
15) $253.15\,K$
#### Convert to Celsius:
16) $-173.15^\circ C$
17) $-73.15^\circ C$
18) $-0.15^\circ C$
19) $76.85^\circ C$
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Parent Tip: Review the logic above to help your child master the concept of temperature conversion worksheet key.
