IGCSE Physics Conversion Worksheet with Metric Prefixes and Unit Conversion Problems

Let's solve each question step by step using the Powers of Ten table provided. The table gives us the prefixes and their corresponding powers of ten, which we will use to convert units.

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1. Convert the following into metres:

We know:
- 1 cm = 0.01 m → $ 10^{-2} $ m
- 1 mm = 0.001 m → $ 10^{-3} $ m
- 1 Mm (megametre) = $ 10^6 $ m

#### a. 10 cm
$$
10 \text{ cm} = 10 \times 10^{-2} \text{ m} = 0.1 \text{ m}
$$

#### b. 5 mm
$$
5 \text{ mm} = 5 \times 10^{-3} \text{ m} = 0.005 \text{ m}
$$

#### c. 1 Mm
$$
1 \text{ Mm} = 1 \times 10^6 \text{ m} = 1,000,000 \text{ m}
$$

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2. Convert the following into kilograms:

We know:
- 1 g = $ 10^{-3} $ kg
- 1 μg = $ 10^{-6} $ g = $ 10^{-9} $ kg
- 1 mg = $ 10^{-3} $ g = $ 10^{-6} $ kg

#### a. 2000 g
$$
2000 \text{ g} = 2000 \times 10^{-3} \text{ kg} = 2 \text{ kg}
$$

#### b. 1 μg
$$
1 \mu\text{g} = 1 \times 10^{-6} \text{ g} = 1 \times 10^{-9} \text{ kg} = 0.000000001 \text{ kg}
$$

#### c. 3 mg
$$
3 \text{ mg} = 3 \times 10^{-3} \text{ g} = 3 \times 10^{-6} \text{ kg} = 0.000003 \text{ kg}
$$

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3. Convert the following into newtons:

We know:
- 1 kN = $ 10^3 $ N
- 1 GN = $ 10^9 $ N
- 1 mN = $ 10^{-3} $ N

#### a. 2.3 kN
$$
2.3 \text{ kN} = 2.3 \times 10^3 \text{ N} = 2300 \text{ N}
$$

#### b. 20 GN
$$
20 \text{ GN} = 20 \times 10^9 \text{ N} = 2 \times 10^{10} \text{ N}
$$

#### c. 300 mN
$$
300 \text{ mN} = 300 \times 10^{-3} \text{ N} = 0.3 \text{ N}
$$

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4. Convert the following into watts:

We know:
- 1 kW = $ 10^3 $ W
- 1 MW = $ 10^6 $ W
- 1 GW = $ 10^9 $ W

#### a. 60 kW
$$
60 \text{ kW} = 60 \times 10^3 \text{ W} = 60,000 \text{ W}
$$

#### b. 45 MW
$$
45 \text{ MW} = 45 \times 10^6 \text{ W} = 4.5 \times 10^7 \text{ W}
$$

#### c. 0.1 GW
$$
0.1 \text{ GW} = 0.1 \times 10^9 \text{ W} = 1 \times 10^8 \text{ W}
$$

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5. Convert the following:

#### a. 0.3 kJ into joules
1 kJ = $ 10^3 $ J
$$
0.3 \text{ kJ} = 0.3 \times 10^3 \text{ J} = 300 \text{ J}
$$

#### b. 90 mA into amps
1 mA = $ 10^{-3} $ A
$$
90 \text{ mA} = 90 \times 10^{-3} \text{ A} = 0.09 \text{ A}
$$

#### c. 800 kHz into hertz
1 kHz = $ 10^3 $ Hz
$$
800 \text{ kHz} = 800 \times 10^3 \text{ Hz} = 8 \times 10^5 \text{ Hz}
$$

#### d. 1 nC into coulombs
1 nC = $ 10^{-9} $ C
$$
1 \text{ nC} = 1 \times 10^{-9} \text{ C}
$$

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✔ Final Answers:

#### 1. Into metres:
a. 10 cm = 0.1 m
b. 5 mm = 0.005 m
c. 1 Mm = 1,000,000 m

#### 2. Into kilograms:
a. 2000 g = 2 kg
b. 1 μg = 1 × 10⁻⁹ kg
c. 3 mg = 3 × 10⁻⁶ kg

#### 3. Into newtons:
a. 2.3 kN = 2300 N
b. 20 GN = 2 × 10¹⁰ N
c. 300 mN = 0.3 N

#### 4. Into watts:
a. 60 kW = 60,000 W
b. 45 MW = 4.5 × 10⁷ W
c. 0.1 GW = 1 × 10⁸ W

#### 5. Convert:
a. 0.3 kJ = 300 J
b. 90 mA = 0.09 A
c. 800 kHz = 8 × 10⁵ Hz
d. 1 nC = 1 × 10⁻⁹ C

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✔ All conversions are based on the standard metric prefixes and powers of ten as shown in the table. Make sure to use scientific notation when appropriate for clarity and precision.