Measurement
1. Length — Metre, Centimetre, Millimetre, Kilometre
Units of Length
| Unit | Symbol | Relation |
|---|---|---|
| Kilometre | km | 1 km = 1000 m |
| Metre | m | 1 m = 100 cm |
| Centimetre | cm | 1 cm = 10 mm |
| Millimetre | mm | 1 mm = 1/10 cm |
'The metre is the STANDARD unit of length. All other units are defined in terms of the metre.'
Conversion Table
| Convert To | Multiply By |
|---|---|
| km → m | × 1000 |
| m → cm | × 100 |
| cm → mm | × 10 |
| m → km | ÷ 1000 |
| cm → m | ÷ 100 |
| mm → cm | ÷ 10 |
Examples
- 3 km = 3 × 1000 = 3000 m
- 450 cm = 450 ÷ 100 = 4.5 m
- 5 m 25 cm = 5 × 100 + 25 = 525 cm
- 6780 m = 6 km 780 m
'When converting from a LARGER unit to a SMALLER unit — MULTIPLY. When converting from a SMALLER unit to a LARGER unit — DIVIDE.'
Addition and Subtraction of Length
Add 4 m 75 cm and 3 m 50 cm:
m cm
4 75
+ 3 50
---------
7 125 cm
125 cm = 1 m 25 cm. Total = 8 m 25 cm.
Subtract 6 m 20 cm from 9 m 10 cm:
Borrow 1 m = 100 cm. 9 m 10 cm = 8 m 110 cm. 8 m 110 cm − 6 m 20 cm = 2 m 90 cm.
2. Mass — Kilogram and Gram
Units of Mass
| Unit | Symbol | Relation |
|---|---|---|
| Kilogram | kg | 1 kg = 1000 g |
| Gram | g | 1 g = 1/1000 kg |
| Milligram | mg | 1 g = 1000 mg |
Conversions
| Convert | Operation | Example |
|---|---|---|
| kg → g | × 1000 | 2.5 kg = 2500 g |
| g → kg | ÷ 1000 | 750 g = 0.75 kg |
| kg g → g | (kg × 1000) + g | 3 kg 450 g = 3450 g |
| g → kg g | ÷ 1000, remainder = g | 3450 g = 3 kg 450 g |
Addition Example
Add 5 kg 600 g and 2 kg 800 g:
kg g
5 600
+ 2 800
--------
7 1400
1400 g = 1 kg 400 g. Total = 8 kg 400 g.
'Always carry when grams reach or exceed 1000 — just like carrying in addition, because 1000 g = 1 kg.'
3. Capacity — Litre and Millilitre
Units of Capacity
| Unit | Symbol | Relation |
|---|---|---|
| Litre | L | 1 L = 1000 mL |
| Millilitre | mL | 1 mL = 1/1000 L |
Conversions
| Convert | Operation | Example |
|---|---|---|
| L → mL | × 1000 | 3 L = 3000 mL |
| mL → L | ÷ 1000 | 2500 mL = 2.5 L |
| L mL → mL | (L × 1000) + mL | 4 L 375 mL = 4375 mL |
Real-Life Examples
- A water bottle holds about 1 L.
- A spoon holds about 5 mL.
- A bucket holds about 10 L.
- A medicine cup holds about 15 mL.
4. Time
Units of Time
| Unit | Relation |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 month | 28, 29, 30, or 31 days |
| 1 year | 365 days (366 in a leap year) |
Converting Time
- 3 hours = 3 × 60 = 180 minutes
- 240 minutes = 240 ÷ 60 = 4 hours
- 2 hours 15 minutes = 2 × 60 + 15 = 135 minutes
- 150 minutes = 2 hours 30 minutes
Adding Time
Add 3 hours 45 minutes and 2 hours 35 minutes:
hr min
3 45
+ 2 35
---------
5 80
80 minutes = 1 hour 20 minutes. Total = 6 hours 20 minutes.
Subtracting Time
Subtract 2 hours 50 minutes from 5 hours 20 minutes:
Borrow 1 hour = 60 minutes. 5 hr 20 min = 4 hr 80 min. 4 hr 80 min − 2 hr 50 min = 2 hr 30 min.
'When borrowing in time, remember that 1 hour = 60 minutes — NOT 100! This is a VERY common mistake.'
12-Hour and 24-Hour Clock
| 12-Hour | 24-Hour |
|---|---|
| 12:00 AM (midnight) | 00:00 |
| 6:00 AM | 06:00 |
| 12:00 PM (noon) | 12:00 |
| 3:00 PM | 15:00 |
| 9:00 PM | 21:00 |
| 11:59 PM | 23:59 |
'For times after 12:59 PM, ADD 12 to convert to 24-hour format. From 24-hour format, SUBTRACT 12 for PM times.'
5. Calendar
Days in Each Month
| Month | Days | Month | Days |
|---|---|---|---|
| January | 31 | July | 31 |
| February | 28 or 29 | August | 31 |
| March | 31 | September | 30 |
| April | 30 | October | 31 |
| May | 31 | November | 30 |
| June | 30 | December | 31 |
'Thirty days have September, April, June, and November. All the rest have thirty-one, save February — it has twenty-eight. In leap year, it gets one more day.'
Leap Year
A year is a LEAP YEAR if:
- It is divisible by 4, AND
- If it is a century year (ending in 00), it must be divisible by 400.
2024 is a leap year. 2025 is NOT a leap year. 2000 was a leap year. 1900 was NOT a leap year.
Key Facts to Remember
- '100 cm = 1 m. 1000 g = 1 kg. 1000 mL = 1 L. MEMORISE these three conversions.'
- To convert a larger unit to a smaller unit — multiply.
- To convert a smaller unit to a larger unit — divide.
- The number of days per month can be found using your knuckles.
- 1 year = 12 months = 52 weeks = 365 days.
Common Mistakes
| Mistake | Why It Is Wrong | Correct Approach |
|---|---|---|
| Multiplying by 100 instead of 1000 for kg→g | Only length uses 100 (m→cm); mass uses 1000 | 2 kg = 2 × 1000 = 2000 g |
| Forgetting to borrow 60 in time subtraction | Borrowing in time is like borrowing 60, not 10 | 1 hour = 60 minutes |
| Adding metres and centimetres directly without conversion | 5 m 75 cm + 2 m 50 cm = 7 m 125 cm → must convert 125 cm | 125 cm = 1 m 25 cm → total = 8 m 25 cm |
| Thinking AM means daytime | AM = Ante Meridiem (before noon) — 12 AM is midnight | AM is from midnight to noon |
Exam Focus (ICSE Class 5)
| Topic | Marks (Typical) | Question Type |
|---|---|---|
| Length conversions (km↔m↔cm) | 3-4 marks | Convert between units |
| Mass and capacity conversions | 3-4 marks | Convert and compare |
| Time calculations | 4-5 marks | Find duration, 12/24-hour conversion |
| Calendar problems | 2-3 marks | Find day, date, or number of days |
| Word problems with mixed units | 4-5 marks | Add/subtract measurements in real life |
Self-Test: 5 Questions
Q1. Convert: (a) 3.75 km to m (b) 2500 g to kg (c) 4 L 350 mL to mL.
Q2. A train leaves at 09:45 and reaches at 14:20. How long is the journey?
Q3. Add: 8 m 90 cm + 6 m 75 cm.
Q4. Riya has 5 kg of flour. She uses 1 kg 750 g for cakes and 2 kg 500 g for bread. How much flour is left?
Q5. How many days are there from January 15 to March 10 in a non-leap year?
Answers
A1. (a) 3.75 km = 3750 m (b) 2500 g = 2.5 kg (c) 4 L 350 mL = 4350 mL.
A2. 09:45 to 14:20 = 4 hours 35 minutes.
A3. 8 m 90 cm + 6 m 75 cm = 14 m 165 cm = 15 m 65 cm.
A4. Used = 1 kg 750 g + 2 kg 500 g = 3 kg 1250 g = 4 kg 250 g. Left = 5 kg − 4 kg 250 g = 750 g.
A5. Jan 16-31 = 16 days. February = 28 days. March 1-10 = 10 days. Total = 16 + 28 + 10 = 54 days.
