IGCSE Physics Conversion Worksheet with Metric Prefixes and Unit Conversion Exercises

Problem: Conversion of Units Using Powers of Ten

The task involves converting various quantities into different units using the provided table of prefixes and their corresponding powers of ten. Let's solve each part step by step.

---

1. Convert the following into metres:

#### a. 10 cm
- Step 1: Recall that "cm" stands for centimetres, and from the table, \(1 \text{ cm} = 10^{-2} \text{ m}\).
- Step 2: Convert \(10 \text{ cm}\) to metres:
\[
10 \text{ cm} = 10 \times 10^{-2} \text{ m} = 10^{1} \times 10^{-2} \text{ m} = 10^{-1} \text{ m} = 0.1 \text{ m}
\]

#### b. 5 mm
- Step 1: Recall that "mm" stands for millimetres, and from the table, \(1 \text{ mm} = 10^{-3} \text{ m}\).
- Step 2: Convert \(5 \text{ mm}\) to metres:
\[
5 \text{ mm} = 5 \times 10^{-3} \text{ m} = 0.005 \text{ m}
\]

#### c. 1 Mm
- Step 1: Recall that "Mm" stands for megametres, and from the table, \(1 \text{ Mm} = 10^6 \text{ m}\).
- Step 2: Convert \(1 \text{ Mm}\) to metres:
\[
1 \text{ Mm} = 1 \times 10^6 \text{ m} = 1,000,000 \text{ m}
\]

Answers for Part 1:
\[
\boxed{0.1 \text{ m}, 0.005 \text{ m}, 1,000,000 \text{ m}}
\]

---

2. Convert the following into kilograms:

#### a. 2000 g
- Step 1: Recall that "g" stands for grams, and from the table, \(1 \text{ g} = 10^{-3} \text{ kg}\).
- Step 2: Convert \(2000 \text{ g}\) to kilograms:
\[
2000 \text{ g} = 2000 \times 10^{-3} \text{ kg} = 2 \text{ kg}
\]

#### b. 1 μg
- Step 1: Recall that "μg" stands for micrograms, and from the table, \(1 \text{ μg} = 10^{-6} \text{ g}\). Since \(1 \text{ g} = 10^{-3} \text{ kg}\), we have:
\[
1 \text{ μg} = 10^{-6} \times 10^{-3} \text{ kg} = 10^{-9} \text{ kg}
\]
- Step 2: Convert \(1 \text{ μg}\) to kilograms:
\[
1 \text{ μg} = 10^{-9} \text{ kg}
\]

#### c. 3 mg
- Step 1: Recall that "mg" stands for milligrams, and from the table, \(1 \text{ mg} = 10^{-3} \text{ g}\). Since \(1 \text{ g} = 10^{-3} \text{ kg}\), we have:
\[
1 \text{ mg} = 10^{-3} \times 10^{-3} \text{ kg} = 10^{-6} \text{ kg}
\]
- Step 2: Convert \(3 \text{ mg}\) to kilograms:
\[
3 \text{ mg} = 3 \times 10^{-6} \text{ kg} = 0.000003 \text{ kg}
\]

Answers for Part 2:
\[
\boxed{2 \text{ kg}, 10^{-9} \text{ kg}, 0.000003 \text{ kg}}
\]

---

3. Convert the following into newtons:

#### a. 2.3 kN
- Step 1: Recall that "kN" stands for kilonewtons, and from the table, \(1 \text{ kN} = 10^3 \text{ N}\).
- Step 2: Convert \(2.3 \text{ kN}\) to newtons:
\[
2.3 \text{ kN} = 2.3 \times 10^3 \text{ N} = 2300 \text{ N}
\]

#### b. 20 GN
- Step 1: Recall that "GN" stands for giganewtons, and from the table, \(1 \text{ GN} = 10^9 \text{ N}\).
- Step 2: Convert \(20 \text{ GN}\) to newtons:
\[
20 \text{ GN} = 20 \times 10^9 \text{ N} = 20,000,000,000 \text{ N}
\]

#### c. 300 mN
- Step 1: Recall that "mN" stands for millinewtons, and from the table, \(1 \text{ mN} = 10^{-3} \text{ N}\).
- Step 2: Convert \(300 \text{ mN}\) to newtons:
\[
300 \text{ mN} = 300 \times 10^{-3} \text{ N} = 0.3 \text{ N}
\]

Answers for Part 3:
\[
\boxed{2300 \text{ N}, 20,000,000,000 \text{ N}, 0.3 \text{ N}}
\]

---

4. Convert the following into watts:

#### a. 60 kW
- Step 1: Recall that "kW" stands for kilowatts, and from the table, \(1 \text{ kW} = 10^3 \text{ W}\).
- Step 2: Convert \(60 \text{ kW}\) to watts:
\[
60 \text{ kW} = 60 \times 10^3 \text{ W} = 60,000 \text{ W}
\]

#### b. 45 MW
- Step 1: Recall that "MW" stands for megawatts, and from the table, \(1 \text{ MW} = 10^6 \text{ W}\).
- Step 2: Convert \(45 \text{ MW}\) to watts:
\[
45 \text{ MW} = 45 \times 10^6 \text{ W} = 45,000,000 \text{ W}
\]

#### c. 0.1 GW
- Step 1: Recall that "GW" stands for gigawatts, and from the table, \(1 \text{ GW} = 10^9 \text{ W}\).
- Step 2: Convert \(0.1 \text{ GW}\) to watts:
\[
0.1 \text{ GW} = 0.1 \times 10^9 \text{ W} = 100,000,000 \text{ W}
\]

Answers for Part 4:
\[
\boxed{60,000 \text{ W}, 45,000,000 \text{ W}, 100,000,000 \text{ W}}
\]

---

5. Convert the following:

#### a. 0.3 kJ into joules
- Step 1: Recall that "kJ" stands for kilojoules, and from the table, \(1 \text{ kJ} = 10^3 \text{ J}\).
- Step 2: Convert \(0.3 \text{ kJ}\) to joules:
\[
0.3 \text{ kJ} = 0.3 \times 10^3 \text{ J} = 300 \text{ J}
\]

#### b. 90 mA into amps
- Step 1: Recall that "mA" stands for milliamps, and from the table, \(1 \text{ mA} = 10^{-3} \text{ A}\).
- Step 2: Convert \(90 \text{ mA}\) to amps:
\[
90 \text{ mA} = 90 \times 10^{-3} \text{ A} = 0.09 \text{ A}
\]

#### c. 800 kHz into hertz
- Step 1: Recall that "kHz" stands for kilohertz, and from the table, \(1 \text{ kHz} = 10^3 \text{ Hz}\).
- Step 2: Convert \(800 \text{ kHz}\) to hertz:
\[
800 \text{ kHz} = 800 \times 10^3 \text{ Hz} = 800,000 \text{ Hz}
\]

#### d. 1 nC into coulombs
- Step 1: Recall that "nC" stands for nanocoulombs, and from the table, \(1 \text{ nC} = 10^{-9} \text{ C}\).
- Step 2: Convert \(1 \text{ nC}\) to coulombs:
\[
1 \text{ nC} = 1 \times 10^{-9} \text{ C} = 10^{-9} \text{ C}
\]

Answers for Part 5:
\[
\boxed{300 \text{ J}, 0.09 \text{ A}, 800,000 \text{ Hz}, 10^{-9} \text{ C}}
\]

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Part 1: } 0.1 \text{ m}, 0.005 \text{ m}, 1,000,000 \text{ m} \\
\text{Part 2: } 2 \text{ kg}, 10^{-9} \text{ kg}, 0.000003 \text{ kg} \\
\text{Part 3: } 2300 \text{ N}, 20,000,000,000 \text{ N}, 0.3 \text{ N} \\
\text{Part 4: } 60,000 \text{ W}, 45,000,000 \text{ W}, 100,000,000 \text{ W} \\
\text{Part 5: } 300 \text{ J}, 0.09 \text{ A}, 800,000 \text{ Hz}, 10^{-9} \text{ C}
\end{array}
}
\]