Metric conversions worksheet with exercises on converting between kilometres, metres, centimetres, millimetres, kilograms, and grams.

Let’s go step by step through each section of the worksheet. We’ll solve every problem carefully and check our work.

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Section A: Kilometres, Metres, Centimetres, and Millimetres

We need to convert between mm, cm, m, km.

Remember:
- 10 mm = 1 cm
- 100 cm = 1 m
- 1000 m = 1 km

So:
- To go from smaller to larger unit → divide
- To go from larger to smaller unit → multiply

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First table (Millimetres ↔ Centimetres)

Convert mm to cm: divide by 10
Convert cm to mm: multiply by 10

- 30 mm = 30 ÷ 10 = 3 cm
- 80 mm = 80 ÷ 10 = 8 cm
- 200 mm = 200 ÷ 10 = 20 cm
- 7 cm = 7 × 10 = 70 mm
- 9.4 cm = 9.4 × 10 = 94 mm
- 13.8 cm = 13.8 × 10 = 138 mm

✔ Checked: All correct.

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Second table (Centimetres ↔ Metres)

Convert cm to m: divide by 100
Convert m to cm: multiply by 100

- 200 cm = 200 ÷ 100 = 2 m
- 420 cm = 420 ÷ 100 = 4.2 m
- 85 cm = 85 ÷ 100 = 0.85 m
- 4 m = 4 × 100 = 400 cm
- 8.9 m = 8.9 × 100 = 890 cm
- 0.5 m = 0.5 × 100 = 50 cm

✔ Checked: All correct.

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Third table (Metres ↔ Kilometres)

Convert m to km: divide by 1000
Convert km to m: multiply by 1000

- 4000 m = 4000 ÷ 1000 = 4 km
- 5800 m = 5800 ÷ 1000 = 5.8 km
- 900 m = 900 ÷ 1000 = 0.9 km
- 7 km = 7 × 1000 = 7000 m
- 8.3 km = 8.3 × 1000 = 8300 m
- 15 km = 15 × 1000 = 15000 m

✔ Checked: All correct.

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Section B: Kilometres and Grams? Wait — it says “Kilometres and Grams” but the tables are about grams and kilograms.

Actually, looking again — Section B is titled “Kilometres and Grams”, but the instruction says: “For each measurement, find its equivalent in kg or g.” So it’s actually grams and kilograms, not kilometres. Probably a typo in the title.

We’ll treat it as Grams ↔ Kilograms

Remember:
- 1000 g = 1 kg
- So: g → kg: divide by 1000; kg → g: multiply by 1000

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Left table (Grams → Kilograms)

- 5000 g = 5000 ÷ 1000 = 5 kg
- 10000 g = 10000 ÷ 1000 = 10 kg
- 1220 g = 1220 ÷ 1000 = 1.22 kg
- 3010 g = 3010 ÷ 1000 = 3.01 kg
- 738 g = 738 ÷ 1000 = 0.738 kg

✔ Checked.

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Right table (Kilograms → Grams)

- 6.05 kg = 6.05 × 1000 = 6050 g
- 170 kg = 170 × 1000 = 170000 g
- 50 kg = 50 × 1000 = 50000 g
- 21.4 kg = 21.4 × 1000 = 21400 g
- 0.371 kg = 0.371 × 1000 = 371 g

✔ Checked.

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Section C: Complete the table by making each row equal.

This means: for each row, the value in one column must equal the value in the other column after conversion.

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Left table: Millimetres ↔ Metres

We know: 1000 mm = 1 m → so mm to m: divide by 1000; m to mm: multiply by 1000

Row 1: 8000 mm = ? m → 8000 ÷ 1000 = 8 m

Row 2: 73300 mm = ? m → 73300 ÷ 1000 = 73.3 m

Row 3: 600 mm = ? m → 600 ÷ 1000 = 0.6 m

Row 4: ? mm = 6 m → 6 × 1000 = 6000 mm

Row 5: ? mm = 14.4 m → 14.4 × 1000 = 14400 mm

Row 6: ? mm = 0.07 m → 0.07 × 1000 = 70 mm

✔ Checked.

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Right table: Centimetres ↔ Kilometres

We know: 100 cm = 1 m, and 1000 m = 1 km → so 100,000 cm = 1 km

Thus:
- cm to km: divide by 100,000
- km to cm: multiply by 100,000

Row 1: 100000 cm = ? km → 100000 ÷ 100000 = 1 km

Row 2: 42000 cm = ? km → 42000 ÷ 100000 = 0.42 km

Row 3: 340 cm = ? km → 340 ÷ 100000 = 0.0034 km

Row 4: ? cm = 5 km → 5 × 100000 = 500000 cm

Row 5: ? cm = 17.1 km → 17.1 × 100000 = 1,710,000 cm

Row 6: ? cm = 0.0058 km → 0.0058 × 100000 = 580 cm

✔ Checked.

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Section D: Word Problems

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Problem 1:

A zoo keeper weighs three new baby koalas at 0.5 kg, 0.616 kg, 706 g.

Work out total weight:

a. in kilograms
b. in grams

Step 1: Convert all to same unit.

Let’s do part (a) first — total in kg.

We have two values in kg: 0.5 kg and 0.616 kg
One in grams: 706 g → convert to kg: 706 ÷ 1000 = 0.706 kg

Now add:
0.5 + 0.616 + 0.706 = ?

Calculate step by step:

0.5 + 0.616 = 1.116
1.116 + 0.706 = 1.822 kg

✔ So answer for (a): 1.822 kg

Now part (b): total in grams

Convert all to grams:

0.5 kg = 0.5 × 1000 = 500 g
0.616 kg = 0.616 × 1000 = 616 g
706 g = 706 g

Add: 500 + 616 + 706

500 + 616 = 1116
1116 + 706 = 1822 g

✔ So answer for (b): 1822 g

Check: 1.822 kg = 1822 g → matches! Good.

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Problem 2:

An athlete runs 8.5 laps around a race track. Each lap is 400 m.

Total distance run:

First, total in metres: 8.5 × 400

Calculate:
8 × 400 = 3200
0.5 × 400 = 200
Total = 3200 + 200 = 3400 m

Now:

a. in kilometres → 3400 ÷ 1000 = 3.4 km

b. in centimetres → 3400 m × 100 = 340,000 cm

(因为 1 m = 100 cm)

✔ Checked.

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Final Answer:

Section A:

*Millimetres ↔ Centimetres:*
- 30 mm = 3 cm
- 80 mm = 8 cm
- 200 mm = 20 cm
- 7 cm = 70 mm
- 9.4 cm = 94 mm
- 13.8 cm = 138 mm

*Centimetres ↔ Metres:*
- 200 cm = 2 m
- 420 cm = 4.2 m
- 85 cm = 0.85 m
- 4 m = 400 cm
- 8.9 m = 890 cm
- 0.5 m = 50 cm

*Metres ↔ Kilometres:*
- 4000 m = 4 km
- 5800 m = 5.8 km
- 900 m = 0.9 km
- 7 km = 7000 m
- 8.3 km = 8300 m
- 15 km = 15000 m

Section B:

*Grams → Kilograms:*
- 5000 g = 5 kg
- 10000 g = 10 kg
- 1220 g = 1.22 kg
- 3010 g = 3.01 kg
- 738 g = 0.738 kg

*Kilograms → Grams:*
- 6.05 kg = 6050 g
- 170 kg = 170000 g
- 50 kg = 50000 g
- 21.4 kg = 21400 g
- 0.371 kg = 371 g

Section C:

*Millimetres ↔ Metres:*
- 8000 mm = 8 m
- 73300 mm = 73.3 m
- 600 mm = 0.6 m
- 6000 mm = 6 m
- 14400 mm = 14.4 m
- 70 mm = 0.07 m

*Centimetres ↔ Kilometres:*
- 100000 cm = 1 km
- 42000 cm = 0.42 km
- 340 cm = 0.0034 km
- 500000 cm = 5 km
- 1710000 cm = 17.1 km
- 580 cm = 0.0058 km

Section D:

1) Total weight of koalas:
a. 1.822 kg
b. 1822 g

2) Total distance run by athlete:
a. 3.4 km
b. 340000 cm