Measurements
Overview
Measurements form the backbone of quantitative reasoning in everyday life and are a staple topic in KAR TET Paper I Mathematics. This topic tests a candidate's understanding of standard units for length, weight (mass), capacity (volume), and time, along with the ability to convert between units and solve practical word problems.
For the TET exam, you must be comfortable with the metric system (metre, gram, litre) and time calculations. Questions typically involve unit conversions, comparing quantities, and applying measurement concepts to real-life situations like shopping, cooking, travel, and scheduling. Mastery here also supports the pedagogy section, as teachers must help young learners connect abstract units to tangible experiences.
Speed and accuracy in conversion are key—most errors stem from misplacing decimal points or confusing unit relationships.
Key Concepts
- Standard units provide a universal language: Length in metres, mass in grams, capacity in litres, and time in seconds/minutes/hours allow consistent communication and comparison.
- Metric system is base-10: Each step up or down multiplies or divides by 10, 100, or 1000 (e.g., 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL).
- Conversion direction matters: To convert a larger unit to a smaller unit, multiply; to convert a smaller unit to a larger unit, divide.
- Time is not metric: Time uses base-60 (60 seconds = 1 minute, 60 minutes = 1 hour) and base-24 (24 hours = 1 day), requiring separate handling.
- Capacity vs Volume: Capacity refers to how much a container can hold (usually liquids), measured in litres/mL; volume refers to space occupied, measured in cubic units (cm³, m³). For liquids, 1 mL = 1 cm³.
- Weight vs Mass: In everyday usage and primary exams, weight and mass are used interchangeably; standard unit is gram (g) or kilogram (kg).
- Estimation and approximation: Primary-level pedagogy emphasises estimation before exact calculation to build number sense.
Formulas / Key Facts
Length
| Relationship | Value |
|---|---|
| 1 kilometre (km) | 1000 metres (m) |
| 1 metre (m) | 100 centimetres (cm) |
| 1 centimetre (cm) | 10 millimetres (mm) |
Weight (Mass)
| Relationship | Value |
|---|---|
| 1 kilogram (kg) | 1000 grams (g) |
| 1 gram (g) | 1000 milligrams (mg) |
| 1 quintal | 100 kg |
| 1 metric ton | 1000 kg |
Capacity / Volume
| Relationship | Value |
|---|---|
| 1 litre (L) | 1000 millilitres (mL) |
| 1 kilolitre (kL) | 1000 litres |
| 1 mL | 1 cm³ (cubic centimetre) |
| 1 L | 1000 cm³ |
Time
| Relationship | Value |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3600 seconds |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 365 days (366 in leap year) |
| 1 year | 12 months |
Quick conversion trick
- Larger → Smaller: Multiply (move decimal right)
- Smaller → Larger: Divide (move decimal left)
Worked Examples
Example 1: Length Conversion
Problem: Convert 3.75 km to metres and then to centimetres.
Solution:
- Step 1: km to m → Multiply by 1000
- 3.75 × 1000 = 3750 m
- Step 2: m to cm → Multiply by 100
- 3750 × 100 = 375000 cm
Answer: 3.75 km = 3750 m = 375000 cm
Example 2: Weight Word Problem
Problem: A shopkeeper has 5 kg 250 g of rice. He sells 2 kg 780 g. How much rice remains?
Solution:
- Step 1: Convert to grams for easier subtraction
- 5 kg 250 g = 5250 g
- 2 kg 780 g = 2780 g
- Step 2: Subtract
- 5250 − 2780 = 2470 g
- Step 3: Convert back
- 2470 g = 2 kg 470 g
Answer: 2 kg 470 g of rice remains
Example 3: Time Calculation
Problem: A train departs at 9:45 AM and arrives at 2:20 PM. What is the journey time?
Solution:
- Step 1: From 9:45 AM to 12:00 noon = 2 hours 15 minutes
- Step 2: From 12:00 noon to 2:20 PM = 2 hours 20 minutes
- Step 3: Total = 2 hr 15 min + 2 hr 20 min = 4 hr 35 min
Answer: 4 hours 35 minutes
Example 4: Capacity Problem
Problem: A tank holds 15 L of water. If 3 L 450 mL is used, how much water is left? Express in mL.
Solution:
- Step 1: Convert all to mL
- 15 L = 15000 mL
- 3 L 450 mL = 3450 mL
- Step 2: Subtract
- 15000 − 3450 = 11550 mL
Answer: 11550 mL (or 11 L 550 mL)
Common Mistakes
- Multiplying when you should divide (or vice versa)
- Wrong: Converting 500 cm to m by multiplying: 500 × 100 = 50000 m
- Correct: Smaller to larger unit → divide: 500 ÷ 100 = 5 m
- Mixing up metric prefixes
- Wrong: Assuming 1 kg = 100 g
- Correct: 1 kg = 1000 g; always recall "kilo" means 1000
- Adding time without regrouping properly
- Wrong: 2 hr 50 min + 1 hr 30 min = 3 hr 80 min (left as is)
- Correct: 80 min = 1 hr 20 min, so answer is 4 hr 20 min
- Ignoring unit consistency in word problems
- Wrong: Adding 2 kg and 500 g directly as 2500
- Correct: Convert both to same unit first (2000 g + 500 g = 2500 g)
- Confusing capacity and volume units in solid vs liquid contexts
- Wrong: Using litres for the volume of a brick
- Correct: Use cm³ or m³ for solids; litres/mL for liquids and container capacity
Quick Reference
- 1 km = 1000 m = 100000 cm
- 1 kg = 1000 g; 1 g = 1000 mg
- 1 L = 1000 mL = 1000 cm³
- 1 hour = 60 min = 3600 sec
- Larger to smaller → multiply; smaller to larger → divide
- Always convert mixed units to a single unit before calculating