Units, Conversions and Time

This lesson covers DfE content statement L1.20 — converting between metric units of length, weight and capacity; working with time; and calculating with money.

---

The Metric System

The metric system is based on powers of 10, which makes converting between units straightforward. At Level 1 you need to convert between metric units only (not metric to imperial).

Length

Unit	Abbreviation	Relationship
Millimetre	mm
Centimetre	cm	1 cm = 10 mm
Metre	m	1 m = 100 cm = 1,000 mm
Kilometre	km	1 km = 1,000 m

graph LR
    km["km"] -->|"× 1,000"| m["m"]
    m -->|"× 100"| cm["cm"]
    cm -->|"× 10"| mm["mm"]
    mm -->|"÷ 10"| cm
    cm -->|"÷ 100"| m
    m -->|"÷ 1,000"| km

Weight (Mass)

Unit	Abbreviation	Relationship
Gram	g
Kilogram	kg	1 kg = 1,000 g
Tonne	t	1 t = 1,000 kg

Capacity (Liquids)

Unit	Abbreviation	Relationship
Millilitre	ml
Litre	l	1 l = 1,000 ml

The Key Conversions to Learn

Conversion	How
cm → mm	× 10
m → cm	× 100
km → m	× 1,000
kg → g	× 1,000
l → ml	× 1,000
mm → cm	÷ 10
cm → m	÷ 100
m → km	÷ 1,000
g → kg	÷ 1,000
ml → l	÷ 1,000

Worked Example — Converting Lengths

Scenario: A door frame is 2.1 m tall. How tall is it in centimetres?

2.1 m × 100 = 210 cm

Worked Example — Converting Weight

Scenario: A recipe needs 750 g of flour. How many kilograms is that?

750 g ÷ 1,000 = 0.75 kg

Worked Example — Converting Capacity

Scenario: A water tank holds 3.5 litres. How many millilitres is that?

3.5 l × 1,000 = 3,500 ml

Worked Example — Adding Different Units

Scenario: You buy 1.2 kg of apples and 450 g of grapes. What is the total weight in grams?

Step 1: Convert 1.2 kg to grams: 1.2 × 1,000 = 1,200 g Step 2: Add: 1,200 + 450 = 1,650 g

Exam Tip: Before adding or subtracting measurements, always convert to the same unit first. It does not matter which unit you choose, as long as they match. Then convert back to the unit the question asks for.

---

Working with Time

Time Facts

Conversion	Value
1 minute	60 seconds
1 hour	60 minutes
1 day	24 hours
1 week	7 days
1 year	365 days (366 in a leap year)

12-Hour and 24-Hour Clock

12-hour	24-hour
12:00 midnight	00:00
6:30 am	06:30
12:00 noon	12:00
1:00 pm	13:00
3:45 pm	15:45
6:15 pm	18:15
11:59 pm	23:59

To convert from 12-hour to 24-hour: For pm times, add 12 to the hour. For am times, the hour stays the same (but write it with a leading zero if needed).

To convert from 24-hour to 12-hour: For hours 13-23, subtract 12 and add "pm". For hours 00-11, use the hour as is and add "am" (00 = 12 midnight).

Worked Example — Converting Times

Scenario: A bus leaves at 14:20. What is this in 12-hour clock?

14 − 12 = 2, so it is 2:20 pm

Worked Example — Calculating Duration

Scenario: A meeting starts at 10:45 am and finishes at 1:15 pm. How long does it last?

Method — count up in stages:

• 10:45 to 11:00 = 15 minutes
• 11:00 to 1:00 pm = 2 hours
• 1:00 pm to 1:15 pm = 15 minutes
• Total = 2 hours and 30 minutes

Worked Example — Timetable

Scenario: A train departs at 09:48 and arrives at 11:23. How long is the journey?

• 09:48 to 10:00 = 12 minutes
• 10:00 to 11:00 = 1 hour
• 11:00 to 11:23 = 23 minutes
• Total = 1 hour 35 minutes

Exam Tip: To find the length of time between two times, count up in stages rather than trying to subtract. Go to the next whole hour, then count the hours, then add the remaining minutes.

---

Converting Between Time Units

Minutes and Hours

Minutes	Hours and Minutes
90 minutes	1 hour 30 minutes
135 minutes	2 hours 15 minutes
200 minutes	3 hours 20 minutes

To convert minutes to hours: Divide by 60. The whole number is the hours; the remainder is the minutes.