Measurement and units — length, mass, time, conversion between systems

Question

Convert 72 km/h to m/s. Why is the SI system preferred over other measurement systems?

(CBSE Class 6 / Class 11 — Measurement and Units)

Unit Conversion Decision Tree

flowchart TD
    A["Unit Conversion Problem"] --> B{What quantity?}
    B -->|Length| C["km ↔ m ↔ cm ↔ mm"]
    B -->|Mass| D["kg ↔ g ↔ mg"]
    B -->|Time| E["hr ↔ min ↔ sec"]
    B -->|Speed| F["km/h ↔ m/s"]
    C --> C1["1 km = 1000 m = 100000 cm"]
    D --> D1["1 kg = 1000 g = 1000000 mg"]
    E --> E1["1 hr = 60 min = 3600 sec"]
    F --> F1["Multiply by 5/18 for km/h to m/s"]
    F --> F2["Multiply by 18/5 for m/s to km/h"]

Solution — Step by Step

Method 1 — Step by step:

$72 \text{ km/h} = 72 \times \dfrac{1000 \text{ m}}{1 \text{ km}} \times \dfrac{1 \text{ h}}{3600 \text{ s}}$

$= 72 \times \dfrac{1000}{3600} = 72 \times \dfrac{5}{18}$

\boxed{72 \text{ km/h} = 20 \text{ m/s}}

Method 2 — Shortcut: multiply by $5/18$ .

$72 \times \dfrac{5}{18} = \dfrac{360}{18} = 20$ m/s

The reverse conversion (m/s to km/h) uses $18/5$ .

The SI (Systeme International) system is universally accepted because:

Consistency — One unit per quantity (metre for length, kilogram for mass, second for time)
Decimal-based — Conversions use powers of 10 (1 km = 1000 m, 1 kg = 1000 g)
Universal — Scientists worldwide use the same units, avoiding confusion
Reproducible — SI units are defined using fundamental constants (speed of light, Planck’s constant)

The seven base SI units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).

Why This Works

Unit conversion is dimensional analysis — we multiply by conversion factors that equal 1 (like 1000 m / 1 km = 1). The original quantity does not change, only the units. The $5/18$ factor for km/h to m/s comes from $1000/3600 = 5/18$ .

Alternative Method — Common Conversions Table

From	To	Multiply by
km/h	m/s	5/18
m/s	km/h	18/5
inches	cm	2.54
miles	km	1.609
pounds	kg	0.4536
feet	m	0.3048

The $5/18$ shortcut is essential for physics problems at every level. Verify it once: $1 \text{ km/h} = 1000/3600 = 5/18 \approx 0.278$ m/s. Now you never need to derive it again. For CBSE Class 11, you also need to know prefixes: nano ( $10^{-9}$ ), micro ( $10^{-6}$ ), milli ( $10^{-3}$ ), kilo ( $10^{3}$ ), mega ( $10^{6}$ ), giga ( $10^{9}$ ).

Common Mistake

The classic error: multiplying by $18/5$ when converting km/h to m/s (or vice versa). Remember: m/s is a “smaller number” than km/h for the same speed (72 km/h = 20 m/s). So going from km/h to m/s should make the number smaller — multiply by $5/18$ (a fraction less than 1). If your converted number is larger, you used the wrong factor.