6.2 Measurement, Units & Conversions

6.2 Measurement, Units & Conversions

Quick Answer: Convert metrics with powers of ten: 1 km = 1,000 m, 1 m = 100 cm, 1 kg = 1,000 g, 1 L = 1,000 mL. Convert time with 60: 1 hour = 60 minutes, 1 minute = 60 seconds. Never mix units in one calculation without converting first.

Mathematics on the Trinidad & Tobago Fire Service entrance paper rewards careful unit handling more than exotic formulas. A correct arithmetic chain fails if you add 2.5 km to 300 m as if both were the same unit. This section drills length, mass, capacity, and time with civilian examples only—travel between towns, shopping, household containers, and ordinary work hours.

The metric mindset

Metric units form a decimal ladder. Moving between neighbouring metric units usually multiplies or divides by 10, 100, or 1,000.

Length

Larger → smaller unit: multiply.
Smaller → larger unit: divide.

Examples:

• 3.2 km → metres: 3.2 × 1,000 = 3,200 m.
• 450 cm → metres: 450 ÷ 100 = 4.5 m.
• 2.75 m → cm: 2.75 × 100 = 275 cm.

Mass (weight in everyday language)

Examples:

• 1.5 kg → g: 1.5 × 1,000 = 1,500 g.
• 750 g → kg: 750 ÷ 1,000 = 0.75 kg.

Capacity (volume of liquids)

Examples:

• 2.4 L → mL: 2.4 × 1,000 = 2,400 mL.
• 350 mL → L: 350 ÷ 1,000 = 0.35 L.

Note: Do not invent fire-pump discharge rates or hose hydraulics. Household tanks, bottles, and buckets are enough for entrance-level capacity problems.

Convert-first rule (the golden habit)

Before adding or comparing:

1. Choose a target unit (often the unit of the answer choices).
2. Convert every measurement to that unit.
3. Then compute.
4. Convert the result only if the answer needs a different unit.

Example — mixed road distances

A courier drives 12 km from Chaguanas toward Couva, then continues another 2,500 m. Total distance in kilometres?

Convert 2,500 m → km: 2,500 ÷ 1,000 = 2.5 km.
Total = 12 + 2.5 = 14.5 km.

If asked in metres: 12 km = 12,000 m; total = 12,000 + 2,500 = 14,500 m. Same physical distance, different unit labels.

Example — shopping packages

Rice packs: one bag is 2.5 kg, another is 750 g. Combined mass in kg?

750 g = 0.75 kg.
Total = 2.5 + 0.75 = 3.25 kg.
In grams: 2,500 + 750 = 3,250 g.

Example — household water containers

A cooler holds 5 L. A jug holds 750 mL. How many full jug-fills empty the cooler?

5 L = 5,000 mL.
Number of jugs = 5,000 ÷ 750 = 6 full jugs with remainder 500 mL (because 750 × 6 = 4,500; 5,000 − 4,500 = 500).
If the question asks “how many jugs are needed to empty completely,” you may need 7 if partial last jug counts as a pour—read the wording carefully (full jugs vs pours required).

Unit rates for fair comparisons

A unit rate answers “per 1 unit”: price per kg, km per hour, pages per minute, TTD per litre.

Unit rate = quantity of interest ÷ related quantity.

Example — best buy

Brand A: 3 kg for $27. Brand B: 2 kg for $20.

Price per kg A = 27 ÷ 3 = $9/kg.
Price per kg B = 20 ÷ 2 = $10/kg.
Brand A is cheaper per kilogram.

Example — fuel efficiency (private car, civilian)

A car travels 240 km on 20 L of fuel.
Rate = 240 ÷ 20 = 12 km per litre.
Fuel for a 90 km trip at the same rate: 90 ÷ 12 = 7.5 L.

Example — typing or form-filling pace

A candidate fills 18 forms in 45 minutes.
Forms per minute = 18 ÷ 45 = 0.4.
Minutes per form = 45 ÷ 18 = 2.5 minutes per form.
At that pace, 30 forms need 30 × 2.5 = 75 minutes.

Time units (not metric powers of ten!)

Time is the classic trap because people apply base-10 thinking.

Hours ↔ minutes

• 2.5 hours = 2 hours + 0.5 × 60 = 2 hours 30 minutes, or 150 minutes total.
• 90 minutes = 90 ÷ 60 = 1.5 hours.
• 1 hour 20 minutes = 1 + 20/60 = 1 1/3 hours = 4/3 hours.

Adding clock times

A bus leaves San Fernando at 6:45 a.m. and arrives in Port of Spain after 1 hour 40 minutes.

6:45 + 1 hour = 7:45; + 40 minutes = 8:25 a.m.

Crossing noon or midnight needs care: 11:30 a.m. + 50 minutes = 12:20 p.m.

Duration from start and end

Shift starts 7:15 a.m., ends 3:45 p.m.

From 7:15 to 12:00 = 4 hours 45 minutes.
From 12:00 to 3:45 = 3 hours 45 minutes.
Total = 8 hours 30 minutes = 8.5 hours.

Alternatively in minutes: 7:15 → 3:45 is from 7×60+15 = 435 minutes past midnight to 15×60+45 = 945 minutes past midnight; difference 945 − 435 = 510 minutes = 510 ÷ 60 = 8.5 hours.

Area and perimeter (light touch)

Entrance arithmetic sometimes uses rectangles (rooms, plots, boards).

• Perimeter of rectangle = 2(L + W).
• Area of rectangle = L × W.

Units:

• Length in m → perimeter in m, area in m².
• If L = 12 m and W = 50 cm, convert W to 0.5 m first: area = 12 × 0.5 = 6 m².

Do not invent irregular fireground geometry; stick to simple shapes if they appear.

Dimensional analysis (cancel the units)

Write conversion factors as fractions equal to 1:

[ 3.6\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} = 3600\ \text{m} ]

The km units cancel. If units do not cancel to the unit you want, the setup is wrong—catch the error before calculating hard numbers.

Multi-step chain

Convert 2.4 km to centimetres:

[ 2.4\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} \times \frac{100\ \text{cm}}{1\ \text{m}} = 2.4 \times 1000 \times 100 = 240{,}000\ \text{cm}. ]

Mixed-unit word problems

Example — three-leg trip

A driver goes 8 km, then 950 m, then 1.2 km. Total in metres?

8 km = 8,000 m; 1.2 km = 1,200 m; + 950 m.
Total = 8,000 + 1,200 + 950 = 10,150 m = 10.15 km.

Example — recipe-scale capacity

A punch recipe needs 250 mL juice per guest. For 12 guests: 250 × 12 = 3,000 mL = 3 L. If bottles are 1.5 L, number of bottles = 3 ÷ 1.5 = 2 bottles.

Example — mass for postage-style comparison (civilian parcels)

Three parcels: 1.2 kg, 800 g, 1 kg 50 g.
Convert all to grams: 1,200 g; 800 g; 1,050 g.
Total = 3,050 g = 3.05 kg.
Heaviest is 1.2 kg (1,200 g).

Common exam traps

Estimation with units

If someone walks about 5 km/h, a 2-hour walk is about 10 km—so an answer of 100 km is absurd without a vehicle. Use real-world magnitude to eliminate options even before exact arithmetic.

Practice discipline for conversions

1. Circle every unit in the stem and in the options.
2. Pick one working unit.
3. Convert, compute, then match the option unit.
4. Re-convert the answer the other way as a check when time allows.

Link forward

Once units are under control, multi-step word problems (§6.3) and rate problems (§6.4) become much safer. Most “hard” arithmetic items are really unit + sequence items: the math operations themselves stay elementary.