Unit Conversions Worksheet 1 - Everett Community College - Free Printable

Here's the complete solution to Unit Conversions Worksheet 1, with clear explanations for each problem.

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1) What are the SI units for distance, mass, and temperature?

- Distance: meter (m)
- Mass: kilogram (kg)
- Temperature: kelvin (K)

> 💡 *Note: While Celsius (°C) is commonly used, the official SI unit for temperature is kelvin (K).*

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2) Write the definitions, symbols, and values for the following SI unit prefixes:

| Prefix | Symbol | Definition (Value) |
|--------|--------|-----------------------------|
| a) kilo | k | 10³ = 1,000 |
| b) centi | c | 10⁻² = 0.01 |
| c) mega | M | 10⁶ = 1,000,000 |
| d) deci | d | 10⁻¹ = 0.1 |
| e) milli | m | 10⁻³ = 0.001 |
| f) micro | μ | 10⁻⁶ = 0.000001 |
| g) nano | n | 10⁻⁹ = 0.000000001 |
| h) pico | p | 10⁻¹² = 0.000000000001 |

> 📝 *These prefixes modify base units (like meter, gram, liter) to represent larger or smaller quantities.*

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3) How many miles are there in 3.45 × 10²⁵ cm?

We need to convert centimeters → miles.

#### Conversion factors:
- 1 inch = 2.54 cm
- 1 foot = 12 inches
- 1 mile = 5280 feet

#### Step-by-step:

First, convert cm → inches:
\[
3.45 \times 10^{25} \text{ cm} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} = \frac{3.45 \times 10^{25}}{2.54} \text{ inches} ≈ 1.358 \times 10^{25} \text{ inches}
\]

Then, inches → feet:
\[
1.358 \times 10^{25} \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} ≈ 1.132 \times 10^{24} \text{ feet}
\]

Finally, feet → miles:
\[
1.132 \times 10^{24} \text{ feet} \times \frac{1 \text{ mile}}{5280 \text{ feet}} ≈ \frac{1.132 \times 10^{24}}{5280} ≈ 2.144 \times 10^{20} \text{ miles}
\]

✔ Final Answer: ≈ 2.14 × 10²⁰ miles

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4) How many meters are there in 89 inches? (2.54 centimeters = 1 inch)

We’ll convert: inches → cm → meters

#### Step-by-step:

Inches → cm:
\[
89 \text{ inches} \times 2.54 \text{ cm/inch} = 226.06 \text{ cm}
\]

cm → meters (since 1 m = 100 cm):
\[
226.06 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 2.2606 \text{ m}
\]

✔ Final Answer: 2.26 meters (rounded to 2 decimal places)

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5) How many feet are there in 75 meters?

We’ll convert: meters → cm → inches → feet

#### Step-by-step:

Meters → cm:
\[
75 \text{ m} \times 100 = 7500 \text{ cm}
\]

cm → inches:
\[
7500 \text{ cm} \times \frac{1 \text{ inch}}{2.54 \text{ cm}} ≈ 2952.76 \text{ inches}
\]

Inches → feet:
\[
2952.76 \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} ≈ 246.06 \text{ feet}
\]

✔ Final Answer: ≈ 246 feet (rounded to nearest whole number)

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6) What temperature is 690°C in Kelvin?

Use the formula:
\[
K = °C + 273.15
\]

So:
\[
K = 690 + 273.15 = 963.15 \text{ K}
\]

✔ Final Answer: 963.15 K

> 🔥 *Note: Kelvin does not use degrees — it’s just “K”.*

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## ✔ Final Answers Summary:

1. Distance: meter (m), Mass: kilogram (kg), Temperature: kelvin (K)
2. See table above.
3. ≈ 2.14 × 10²⁰ miles
4. 2.26 meters
5. ≈ 246 feet
6. 963.15 K

Let me know if you’d like these steps visualized or explained further!