Measurement — Length, Mass, Capacity, and Time
1. Length
Standard Units:
- Kilometre (km) — for long distances (between cities)
- Metre (m) — for medium lengths (height of a room)
- Centimetre (cm) — for small lengths (length of a pencil)
- Millimetre (mm) — for very small lengths (thickness of a coin)
Conversions:
| From | To | Multiply/Divide | Example |
|---|---|---|---|
| km → m | Multiply by 1000 | 5 km = 5 × 1000 = 5000 m | |
| m → cm | Multiply by 100 | 3 m = 3 × 100 = 300 cm | |
| cm → mm | Multiply by 10 | 8 cm = 8 × 10 = 80 mm | |
| m → km | Divide by 1000 | 4000 m = 4 km | |
| cm → m | Divide by 100 | 250 cm = 2.5 m | |
| mm → cm | Divide by 10 | 45 mm = 4.5 cm |
'When converting from a BIGGER unit to a SMALLER unit, MULTIPLY. When converting from a SMALLER to a BIGGER, DIVIDE.'
Addition of Length:
Add 3 km 450 m + 2 km 380 m
| km | m |
|---|---|
| 3 | 450 |
| +2 | 380 |
| 5 | 830 |
Answer: 5 km 830 m
Subtraction of Length:
Subtract 2 km 380 m from 5 km 600 m
| km | m |
|---|---|
| 5 | 600 |
| -2 | 380 |
| 3 | 220 |
Answer: 3 km 220 m
2. Mass (Weight)
Standard Units:
- Kilogram (kg) — for heavier objects (a bag of rice)
- Gram (g) — for lighter objects (a pencil)
- Milligram (mg) — for very light objects (a grain of salt)
Conversions:
| From | To | Multiply/Divide | Example |
|---|---|---|---|
| kg → g | Multiply by 1000 | 3 kg = 3000 g | |
| g → mg | Multiply by 1000 | 2 g = 2000 mg | |
| g → kg | Divide by 1000 | 5000 g = 5 kg |
Key Fact:
'1 kilogram = 1000 grams. Remember: KILO means THOUSAND.'
Word Problem:
A bag of rice weighs 5 kg 750 g. A bag of wheat weighs 3 kg 500 g. What is their total weight?
Solution: 5 kg 750 g + 3 kg 500 g = 9 kg 250 g
3. Capacity
Standard Units:
- Litre (L) — for liquids (water, milk, oil)
- Millilitre (mL) — for small amounts of liquid (medicine)
Conversions:
| From | To | Multiply/Divide | Example |
|---|---|---|---|
| L → mL | Multiply by 1000 | 2 L = 2000 mL | |
| mL → L | Divide by 1000 | 3000 mL = 3 L |
Key Fact:
'1 litre = 1000 millilitres. MILLI means THOUSANDTH.'
Word Problem:
A water tank contains 25 L 500 mL of water. Another 12 L 750 mL is added. What is the total?
Solution: 25 L 500 mL + 12 L 750 mL = 38 L 250 mL
4. Time
Basic Units:
- 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)
Reading the Clock:
| Time | On Clock | Words |
|---|---|---|
| 3:00 | Hour hand at 3, Minute hand at 12 | Three o'clock |
| 3:15 | Hour hand past 3, Minute hand at 3 | Quarter past three |
| 3:30 | Hour hand between 3 and 4, Minute hand at 6 | Half past three |
| 3:45 | Hour hand near 4, Minute hand at 9 | Quarter to four |
AM and PM:
- AM — Midnight to Noon (12:00 AM to 11:59 AM) — Morning
- PM — Noon to Midnight (12:00 PM to 11:59 PM) — Afternoon/Evening/Night
| 12-hour clock | 24-hour clock |
|---|---|
| 6:00 AM | 06:00 |
| 12:00 PM (Noon) | 12:00 |
| 3:30 PM | 15:30 |
| 9:00 PM | 21:00 |
| 12:00 AM (Midnight) | 00:00 |
'For PM times after 12:59, ADD 12 to get the 24-hour format. 3:00 PM = 15:00.'
Elapsed Time:
School starts at 8:30 AM and ends at 2:30 PM. How long is the school day?
Solution: From 8:30 AM to 2:30 PM = 6 hours.
5. Calendar
Days in Each Month:
'Thirty days have September, April, June, and November. All the rest have thirty-one — except February, which has twenty-eight (or twenty-nine in a leap year).'
| 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 |
Leap Year:
A leap year has 366 days. It occurs EVERY 4 years.
'If a year is divisible by 4, it is usually a leap year. 2024 and 2028 are leap years.'
6. Word Problems
Problem 1:
A cloth shop sells 23 m 75 cm of fabric in the morning and 34 m 50 cm in the afternoon. What is the total fabric sold?
Solution: 23 m 75 cm + 34 m 50 cm = 58 m 25 cm
Problem 2:
A train leaves at 9:45 AM and reaches at 1:30 PM. How long is the journey?
Solution: 9:45 AM to 12:00 PM = 2 hours 15 min, then to 1:30 PM = 1 hour 30 min. Total = 3 hours 45 minutes.
Problem 3:
A bottle contains 1 L 250 mL of juice. How many glasses of 150 mL each can be filled?
Solution: 1 L 250 mL = 1250 mL. 1250 ÷ 150 = 8 glasses (with 50 mL left).
7. Common Mistakes
- Wrong conversion direction: 'When converting km to m, MULTIPLY by 1000 (4 km = 4000 m). When converting m to km, DIVIDE (4000 m = 4 km). Don't mix them up!'
- Forgetting units: 'Always write the unit (km, m, cm, kg, g, L, mL) with your answer. 5 is just a number — 5 km means something!'
- AM/PM confusion: '12:00 PM is NOON (lunchtime). 12:00 AM is MIDNIGHT (when you're sleeping). Many students get this backward!'
- Calendar mistakes: 'September, April, June, and November have 30 days. February has 28 days (29 in a leap year). All others have 31.'
8. Key Facts to Remember
- '1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.'
- '1 kg = 1000 g. 1 L = 1000 mL.'
- '1 hour = 60 minutes. 1 minute = 60 seconds.'
- 'A leap year has 366 days (February 29).'
- 'Bigger to smaller → MULTIPLY. Smaller to bigger → DIVIDE.'
9. Self-Test
Q1: Convert: (a) 5 km = ? m (b) 300 cm = ? m (c) 4 kg = ? g
Q2: Convert: (a) 2 L = ? mL (b) 5000 mL = ? L
Q3: Add: 4 kg 350 g + 2 kg 750 g
Q4: Subtract: 8 m 45 cm - 3 m 20 cm
Q5: What time is 3 hours after 10:30 AM?
Q6: How many days are there in the month of June?
Q7: A movie starts at 4:45 PM and lasts 2 hours 30 minutes. When does it end?
Q8: Which is heavier — 5 kg of feathers or 5 kg of iron? Why?
Answers:
A1: (a) 5000 m (b) 3 m (c) 4000 g A2: (a) 2000 mL (b) 5 L A3: 7 kg 100 g A4: 5 m 25 cm A5: 1:30 PM A6: 30 days A7: 7:15 PM A8: Both are the SAME — 5 kg each! Weight is weight, regardless of material.
