Measurement — Class 5 IMO

Advanced Conversions

Units link in steps. For length, 1 km = 1000 m and 1 m = 100 cm, so 1 km = 1,00,000 cm. For weight, 1 kg = 1000 g and 1 g = 1000 mg. For capacity, 1 L = 1000 mL.

To change a bigger unit to a smaller one, multiply; to change a smaller unit to a bigger one, divide.

Example 1: How many centimetres are there in 1 km?

1 km = 1000 m = 1,00,000 cm.

Example 2: Change 5 g into milligrams.

5 × 1000 = 5000 mg.

Quick recap

1 km = 1000 m = 1,00,000 cm; 1 kg = 1000 g; 1 g = 1000 mg; 1 L = 1000 mL.
Bigger to smaller: multiply. Smaller to bigger: divide.

✓ Quick check

1 km = ___ m?

1 km = 1000 m.

3 L = ___ mL?

3 × 1000 = 3000 mL.

Operations with Mixed Units

To add or subtract mixed units, work on each unit separately and regroup when needed. For 2 km 500 m + 1 km 600 m, the metres make 1100 m = 1 km 100 m, so the total is 4 km 100 m.

Example 1: Add 2 km 500 m + 1 km 600 m.

500 + 600 = 1100 m = 1 km 100 m, so total 4 km 100 m.

Example 2: Subtract 5 kg − 1 kg 250 g.

5 kg = 4 kg 1000 g; 4 kg 1000 g − 1 kg 250 g = 3 kg 750 g.

Quick recap

Work on each unit separately, regrouping when needed.
1000 m makes 1 km; 1000 g makes 1 kg; 1000 mL makes 1 L.

✓ Quick check

1 m 50 cm + 2 m 70 cm = ?

50 + 70 = 120 cm = 1 m 20 cm, so total 4 m 20 cm.

3 L 200 mL − 1 L 500 mL = ?

Borrow: 2 L 1200 mL − 1 L 500 mL = 1 L 700 mL.

Speed, Distance & Time

Speed tells how fast something moves: speed = distance ÷ time. A car going 100 km in 2 hours travels at 100 ÷ 2 = 50 km/hr.

We can rearrange this: distance = speed × time, and time = distance ÷ speed.

Example 1: A car covers 120 km in 3 hours. What is its speed?

120 ÷ 3 = 40 km/hr.

Example 2: A car travels at 60 km/hr for 2 hours. How far does it go?

60 × 2 = 120 km.

Quick recap

speed = distance ÷ time.
distance = speed × time; time = distance ÷ speed.

✓ Quick check

A bus covers 150 km in 3 hours. What is its speed?

150 ÷ 3 = 50 km/hr.

A car travels at 40 km/hr for 4 hours. How far does it go?

40 × 4 = 160 km.