Farenheit and Celsius Converions PDF | Download Free PDF ... - Free Printable

It looks like you've uploaded a Temperature Conversion Worksheet that asks you to convert temperatures between Fahrenheit (°F) and Celsius (°C) using the standard conversion formulas:

🔹 Formulas:

- To convert Fahrenheit to Celsius:
$$
°C = \frac{5}{9} (°F - 32)
$$
- To convert Celsius to Fahrenheit:
$$
°F = \frac{9}{5} °C + 32
$$

Let’s go through each question step by step.

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✔ Part 1: Convert from Fahrenheit to Celsius

#### a) 40°F
$$
°C = \frac{5}{9}(40 - 32) = \frac{5}{9}(8) = \frac{40}{9} ≈ 4.4°C
$$

✔ Answer: 4.4°C

#### b) 0°F
$$
°C = \frac{5}{9}(0 - 32) = \frac{5}{9}(-32) = -\frac{160}{9} ≈ -17.8°C
$$

✔ Answer: -17.8°C

#### c) 32°F (freezing point)
$$
°C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0°C
$$

✔ Answer: 0°C

#### d) 98°F (room temperature)
$$
°C = \frac{5}{9}(98 - 32) = \frac{5}{9}(66) = \frac{330}{9} ≈ 36.7°C
$$

✔ Answer: 36.7°C

#### e) 98.6°F (body temperature)
$$
°C = \frac{5}{9}(98.6 - 32) = \frac{5}{9}(66.6) = \frac{333}{9} = 37°C
$$

✔ Answer: 37°C

#### f) 100°F
$$
°C = \frac{5}{9}(100 - 32) = \frac{5}{9}(68) = \frac{340}{9} ≈ 37.8°C
$$

✔ Answer: 37.8°C

#### g) 212°F (boiling point)
$$
°C = \frac{5}{9}(212 - 32) = \frac{5}{9}(180) = 100°C
$$

✔ Answer: 100°C

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✔ Part 2: Convert from Celsius to Fahrenheit

#### a) 40°C
$$
°F = \frac{9}{5}(40) + 32 = 72 + 32 = 104°F
$$

✔ Answer: 104°F

#### b) 0°C (freezing point)
$$
°F = \frac{9}{5}(0) + 32 = 0 + 32 = 32°F
$$

✔ Answer: 32°F

#### c) 32°C
$$
°F = \frac{9}{5}(32) + 32 = 57.6 + 32 = 89.6°F
$$

✔ Answer: 89.6°F

#### d) 39°C
$$
°F = \frac{9}{5}(39) + 32 = 70.2 + 32 = 102.2°F
$$

✔ Answer: 102.2°F

#### e) 98.6°C
Wait — this is very hot, not typical body temp. Let's compute it anyway:
$$
°F = \frac{9}{5}(98.6) + 32 = 177.48 + 32 = 209.48°F
$$

✔ Answer: ~209.5°F
(Note: This is not normal body temperature in °C — human body temp is ~37°C, not 98.6°C.)

#### f) 100°C (boiling point)
$$
°F = \frac{9}{5}(100) + 32 = 180 + 32 = 212°F
$$

✔ Answer: 212°F

#### g) 212°C
$$
°F = \frac{9}{5}(212) + 32 = 381.6 + 32 = 413.6°F
$$

✔ Answer: 413.6°F

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✔ Final Answers Summary:

#### Part 1: °F → °C
| °F | °C |
|-----------|------------|
| 40°F | 4.4°C |
| 0°F | -17.8°C |
| 32°F | 0°C |
| 98°F | 36.7°C |
| 98.6°F | 37°C |
| 100°F | 37.8°C |
| 212°F | 100°C |

#### Part 2: °C → °F
| °C | °F |
|-----------|------------|
| 40°C | 104°F |
| 0°C | 32°F |
| 32°C | 89.6°F |
| 39°C | 102.2°F |
| 98.6°C | 209.5°F |
| 100°C | 212°F |
| 212°C | 413.6°F |

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📝 Notes:

- The freezing point of water is 0°C = 32°F
- The boiling point of water is 100°C = 212°F
- Normal human body temperature is 37°C = 98.6°F
- The worksheet has a typo: "98.6°C" is extremely high — likely meant to be 37°C or 98.6°F.

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