Worksheet on understanding and using SI prefixes for unit conversion and measurement.

Problem Analysis:

The task involves completing a table of prefixes used in the metric system, understanding their decimal equivalents, and answering questions related to the use of these prefixes. The table provided includes some examples, such as "G" (giga) and "da" (deca), along with their corresponding powers of 10.

#### Step 1: Complete the Table
We need to fill in the missing entries in the table. Here is the completed table:

| Symbol | Prefix Name | Power of 10 | Decimal Equivalent |
|------------|------------------|-----------------|------------------------|
| G | giga | $10^9$ | $1,000,000,000$ |
| da | deca | $10^1$ | $10$ |
| h | hecto | $10^2$ | $100$ |
| d | deci | $10^{-1}$ | $0.1$ |
| c | centi | $10^{-2}$ | $0.01$ |
| m | milli | $10^{-3}$ | $0.001$ |
| μ | micro | $10^{-6}$ | $0.000001$ |
| n | nano | $10^{-9}$ | $0.000000001$ |

#### Explanation:
- h (hecto): Represents $10^2$, which is 100.
- d (deci): Represents $10^{-1}$, which is 0.1.
- c (centi): Represents $10^{-2}$, which is 0.01.
- m (milli): Represents $10^{-3}$, which is 0.001.
- μ (micro): Represents $10^{-6}$, which is 0.000001.
- n (nano): Represents $10^{-9}$, which is 0.000000001.

---

Step 2: Answer the Questions

#### Question 2(a): The largest unit among the following:
- Options: kilogram, megagram, gram, nanogram
- Answer: Megagram ($10^6$ grams)

#### Explanation:
- Kilogram = $10^3$ grams
- Megagram = $10^6$ grams
- Gram = $10^0$ grams
- Nanogram = $10^{-9}$ grams

Among these, the largest unit is the megagram.

---

#### Question 2(b): How many milligrams are in a gram?
- Answer: 1,000 milligrams

#### Explanation:
- 1 gram = $10^0$ grams
- 1 milligram = $10^{-3}$ grams
- Therefore, $1 \text{ gram} = 10^3 \text{ milligrams} = 1,000 \text{ milligrams}$.

---

#### Question 2(c): A meter has how many cm?
- Answer: 100 cm

#### Explanation:
- 1 meter = $10^0$ meters
- 1 centimeter = $10^{-2}$ meters
- Therefore, $1 \text{ meter} = 10^2 \text{ cm} = 100 \text{ cm}$.

---

#### Question 2(d): How many bricks in a megabrick?
- Answer: This question is ambiguous because "megabrick" is not a standard term. However, if we interpret it as meaning "a million bricks," then:
- Answer: 1,000,000 bricks

#### Explanation:
- "Mega-" represents $10^6$, so a "megabrick" would imply $10^6$ bricks, or 1,000,000 bricks.

---

Step 3: Estimation Using Prefixes and Units

#### Question 3(a): Estimate the size of each example using appropriate prefixes and units:
- Your height: Approximately 1.7 meters (or 170 cm)
- Your mass: Approximately 70 kilograms
- Mass of a person: Approximately 70 kilograms
- Width of little finger: Approximately 1 cm
- Distance across town: Approximately 10 kilometers
- Thickness of a dime: Approximately 1 mm

#### Explanation:
- Height: Most people are around 1.7 meters tall.
- Mass: An average adult weighs about 70 kilograms.
- Little finger width: Typically around 1 cm.
- Distance across town: Depending on the town, this could be around 10 kilometers.
- Thickness of a dime: A dime is very thin, approximately 1 mm.

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Completed Table:} \\
\begin{array}{|c|c|c|c|}
\hline
\text{Symbol} & \text{Prefix Name} & \text{Power of 10} & \text{Decimal Equivalent} \\
\hline
G & \text{giga} & 10^9 & 1,000,000,000 \\
\hline
da & \text{deca} & 10^1 & 10 \\
\hline
h & \text{hecto} & 10^2 & 100 \\
\hline
d & \text{deci} & 10^{-1} & 0.1 \\
\hline
c & \text{centi} & 10^{-2} & 0.01 \\
\hline
m & \text{milli} & 10^{-3} & 0.001 \\
\hline
\mu & \text{micro} & 10^{-6} & 0.000001 \\
\hline
n & \text{nano} & 10^{-9} & 0.000000001 \\
\hline
\end{array} \\
\text{Question 2(a): Megagram} \\
\text{Question 2(b): 1,000 milligrams} \\
\text{Question 2(c): 100 cm} \\
\text{Question 2(d): 1,000,000 bricks} \\
\text{Question 3(a):} \\
\text{- Your height: 1.7 meters} \\
\text{- Your mass: 70 kilograms} \\
\text{- Mass of a person: 70 kilograms} \\
\text{- Width of little finger: 1 cm} \\
\text{- Distance across town: 10 kilometers} \\
\text{- Thickness of a dime: 1 mm} \\
\end{array}
}
\]