Mathematics • Class 6 Appendix-II Item 14 150 Mins Overall

Conversion of Units

Pointwise AISSEE Class 6 Mathematics guide for Conversion of Units (Topic 14). Master King Henry prefix ladder, km-m-cm-mm conversions, kg-g-mg weight, capacity mL-L, area m² to cm², and hours to seconds.

Overview & Fundamental Concept

Pointwise AISSEE Class 6 Mathematics guide for Conversion of Units (Topic 14). Master King Henry prefix ladder, km-m-cm-mm conversions, kg-g-mg weight, capacity mL-L, area m² to cm², and hours to seconds.

Official Syllabus Coverage Breakdown
Syllabus Item Prescribed Scope Exam Relevance & Pedagogical Objective
Item 14 Metric units of length (km, m, cm, mm), mass (kg, g, mg), capacity (kL, L, mL), time (hours, minutes, seconds), and money (rupees, paise). Master the metric ladder, prefix multipliers, length, mass, and capacity conversions, square/cubic metric scaling, and time-money equivalences for AISSEE Class VI.
1. The Universal Metric Prefix Ladder
  • The Metric System Hierarchy: The metric system is a base-10 decimal system of weights and measures. Every consecutive step on the metric ladder represents a power of 10.
  • The 7 Standard Metric Prefixes:
  • • Kilo (k): $1,000$ times base unit ($10^3$)
  • • Hecto (h): $100$ times base unit ($10^2$)
  • • Deca (da): $10$ times base unit ($10^1$)
  • • Base Unit: Meter (Length), Gram (Mass), Liter (Capacity) ($10^0 = 1$)
  • • Deci (d): $\frac{1}{10} = 0.1$ of base unit ($10^{-1}$)
  • • Centi (c): $\frac{1}{100} = 0.01$ of base unit ($10^{-2}$)
  • • Milli (m): $\frac{1}{1,000} = 0.001$ of base unit ($10^{-3}$)
  • Conversion Operation Rule:
    • Big to Small (Step Down): Multiply by 10 for each step downward.
    • Small to Big (Step Up): Divide by 10 for each step upward.
PrefixSymbolRelative ValueLength (m)Mass (g)Capacity (L)
Kilok1,000Kilometer (km)Kilogram (kg)Kiloliter (kL)
Hectoh100Hectometer (hm)Hectogram (hg)Hectoliter (hL)
Decada10Decameter (dam)Decagram (dag)Decaliter (daL)
Base Unit-1Meter (m)Gram (g)Liter (L)
Decid0.1Decimeter (dm)Decigram (dg)Deciliter (dL)
Centic0.01Centimeter (cm)Centigram (cg)Centiliter (cL)
Millim0.001Millimeter (mm)Milligram (mg)Milliliter (mL)
Cadet Mnemonic • King Henry Died Memory Key

Remember metric prefixes from largest to smallest:

  • King • Kilo ($1000$)
  • Henry • Hecto ($100$)
  • Died • Deca ($10$)
  • Mother • Meter/Base ($1$)
  • Didn't • Deci ($0.1$)
  • Cry • Centi ($0.01$)
  • Much • Milli ($0.001$)
2. Length, Mass, Capacity & Commercial Units
  • Length Standards:
    • $1\text{ km} = 1,000\text{ m}$
    • $1\text{ m} = 100\text{ cm} = 1,000\text{ mm}$
    • $1\text{ cm} = 10\text{ mm}$
  • Mass (Weight) Standards:
    • $1\text{ kg} = 1,000\text{ g}$
    • $1\text{ g} = 1,000\text{ mg}$
    • 1 Quintal $= 100\text{ kg}$
    • 1 Metric Ton (Tonne) $= 1,000\text{ kg} = 10\text{ Quintals}$
  • Capacity Standards:
    • $1\text{ kL} = 1,000\text{ L}$
    • $1\text{ L} = 1,000\text{ mL} = 1,000\text{ cm}^3$
    • $1\text{ m}^3 = 1,000\text{ L}$ (Capacity of a cubic meter water tank)
  • Area & Volume Squared/Cubic Metric Scaling:
    • $1\text{ m}^2 = (100\text{ cm}) \times (100\text{ cm}) = 10,000\text{ cm}^2$
    • $1\text{ cm}^2 = 100\text{ mm}^2$
    • $1\text{ m}^3 = 100 \times 100 \times 100 = 1,000,000\text{ cm}^3$
AISSEE Trap Alert • The Area Metric Conversion Trap

1 m = 100 cm, BUT 1 m² is NOT 100 cm²! 1 m² = (100 cm) × (100 cm) = 10,000 cm². Squaring the unit means squaring the multiplier!

3. Time & Currency Metric Conversions
  • Currency: $1\text{ Rupee (₹)} = 100\text{ Paise}$. To convert paise to rupees, divide by 100 (shift decimal two places left: $450\text{ paise} = ₹4.50$).
  • Time Standards:
    • $1\text{ Day} = 24\text{ Hours}$
    • $1\text{ Hour} = 60\text{ Minutes} = 3,600\text{ Seconds}$
    • $1\text{ Minute} = 60\text{ Seconds}$
    • $1\text{ Normal Year} = 365\text{ Days} = 52\text{ Weeks} + 1\text{ Day}$
    • $1\text{ Leap Year} = 366\text{ Days} = 52\text{ Weeks} + 2\text{ Days}$ (February has 29 days; years divisible by 4, century years divisible by 400).
Exam Trick • Hours to Seconds in One Step
To convert hours directly to seconds, multiply by 3,600 (not 60!). 2.5 hours = 2.5 × 3,600 = 9,000 seconds.
Visual Concept Blueprint • Vector Architecture
METRIC PREFIX LADDER: KILO → HECTO → DECA → BASE → DECI → CENTI → MILLI kilo-×1000 hecto-×100 deca-×10 BASEm, L, g deci-÷10 centi-÷100 milli-÷1000 ← Multiply by 10 per step (Big to Small) Divide by 10 per step (Small to Big) →

Speed Shortcuts & Mental Calculation Strategies

Master these high-yield time-saving heuristics curated by top AISSEE scorers to eliminate calculation bottlenecks and answer questions in under 45 seconds.

Shortcut Technique 1: Decimal Movement Anchor

Multiplying by $10^k$ shifts decimal $k$ places right (Big to Small). Dividing shifts decimal $k$ places left (Small to Big).

Shortcut Technique 2: Composite Unit Reduction

Convert mixed expressions like '3 kg 45 g' into a single decimal unit before operating: 3 kg + 0.045 kg = 3.045 kg.

Shortcut Technique 3: Volume to Capacity Bridge

Remember the universal liquid bridge: $1\text{ cm}^3 = 1\text{ mL}$ and $1,000\text{ cm}^3 = 1\text{ Liter}$.

Interactive 3D Revision Flashcards Deck

Click any card to flip and reveal the key exam rule or topper secret.

REVISION FLASHCARD
What is the core rule & definition for Conversion of Units?
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CADET MEMORY KEY
Length: 1\text{ km} = 1000\text{ m}, \quad 1\text{ m} = 100\text{ cm} = 1000\text{ mm}
Click to Flip Back
REVISION FLASHCARD
Cadet Shortcut: How to solve Conversion of Units in under 30 seconds?
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CADET MEMORY KEY
Fast MCQ Elimination: Check the last digit (unit digit) and estimate the order of magnitude to eliminate 2 distractors in under 10 seconds.
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REVISION FLASHCARD
Exam Trap Alert: What pitfall do most candidates fall into?
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CADET MEMORY KEY
Big to Small: Multiply when converting from larger units to smaller units (km to m: × 1000).
Click to Flip Back
REVISION FLASHCARD
Rapid Memory Anchor for AISSEE Hall Recall:
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CADET MEMORY KEY
Small to Big: Divide when converting from smaller units to larger units (g to kg: ÷ 1000).
Click to Flip Back
REVISION FLASHCARD
How many centimeters are there in 4.5 kilometers?
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CADET MEMORY KEY
4.5 km = 4.5 × 1,000 m = 4,500 m. 4,500 m = 4,500 × 100 cm = 4,50,000 cm.
Click to Flip Back
Common Traps & Examination Pitfalls

Avoid the Speed-Guess Trap: Under AISSEE pressure, candidates frequently misread units (e.g., mixing metres and centimetres, or per hour and per second) and confuse complementary ($90^\circ$) with supplementary ($180^\circ$) angles. Read every stem carefully and check units before selecting your OMR option.

Key Identities & Formulas

Length Metric Steps
$$1\text{ km} = 10^3\text{ m} = 10^5\text{ cm} = 10^6\text{ mm}$$
Standard metric distance scale.
Mass Commercial Measures
$$1\text{ Tonne} = 10\text{ Quintals} = 1,000\text{ kg}$$
Commercial agricultural weight units.
Area & Volume Multipliers
$$1\text{ m}^2 = 10^4\text{ cm}^2, \quad 1\text{ m}^3 = 10^3\text{ L} = 10^6\text{ cm}^3$$
2D and 3D metric power expansions.
Step-by-Step Solved Examination Models
Solved Example 1 Model Problem
Convert a speed of $72\text{ km/h}$ into metres per second (m/s).
(A) 20 m/s
(B) 25 m/s
(C) 18 m/s
(D) 15 m/s
Detailed Solution: To convert km/h to m/s, multiply by $\frac{5}{18}$: $72 \times \frac{5}{18} = 4 \times 5 = 20\text{ m/s}$.
Solved Example 2 Model Problem
A tin contains $15\text{ litres } 750\text{ ml}$ of oil. How many millilitres (ml) is this in total?
(A) 15,750 ml
(B) 1,575 ml
(C) 157,500 ml
(D) 15.75 ml
Detailed Solution: $1\text{ litre} = 1,000\text{ ml}$. $15\text{ litres} = 15 \times 1,000 = 15,000\text{ ml}$. Total = $15,000 + 750 = 15,750\text{ ml}$.
Solved Example 3 Model Problem
A water tank holds 2.4 kiloliters of water. If a family consumes 800 liters of water daily, for how many days will the full tank of water last?
(A) 3 days
(B) 4 days
(C) 2.5 days
(D) 5 days
Detailed Solution: 1. Convert tank capacity from kiloliters to liters: $1\text{ kL} = 1,000\text{ L}$.
2. Tank capacity $= 2.4 \times 1,000 = 2,400\text{ liters}$.
3. Daily consumption $= 800\text{ liters}$.
4. Number of days water will last $= \frac{2,400}{800} = 3\text{ days}$. Correct Option is (A).

AISSEE High-Yield Practice Drills (10 Questions)

Simulated exam drill matching NTA question style, difficulty, and phrasing. Click an option for instant feedback and pedagogical explanation.

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Question 1 of 10 Exam Standard
Convert 25 m/s into km/h.
Correct Answer: Option (A)
To convert m/s to km/h, multiply by $\frac{18}{5}$: $25 \times \frac{18}{5} = 5 \times 18 = 90\text{ km/h}$.
Question 2 of 10 Exam Standard
How many metres are there in $4.5\text{ km}$?
Correct Answer: Option (A)
$1\text{ km} = 1,000\text{ m}$. $4.5 \times 1,000 = 4,500\text{ m}$.
Question 3 of 10 Exam Standard
Convert $3,450\text{ grams}$ into kilograms.
Correct Answer: Option (A)
$1\text{ kg} = 1,000\text{ g}$. $3450 / 1000 = 3.45\text{ kg}$.
Question 4 of 10 Exam Standard
How many square centimetres are there in 1 square metre?
Correct Answer: Option (A)
$1\text{ m} = 100\text{ cm}$. $1\text{ sq m} = 100\text{ cm} \times 100\text{ cm} = 10,000\text{ sq cm}$.
Question 5 of 10 Exam Standard
Convert 3 hours 45 minutes into minutes.
Correct Answer: Option (A)
$3\text{ hours} = 3 \times 60 = 180\text{ mins}$. Total = $180 + 45 = 225\text{ minutes}$.
Question 6 of 10 Exam Standard
How many millilitres make $3.25\text{ litres}$?
Correct Answer: Option (A)
$3.25 \times 1,000 = 3,250\text{ ml}$.
Question 7 of 10 Exam Standard
Convert $750\text{ cm}$ into metres.
Correct Answer: Option (A)
$100\text{ cm} = 1\text{ m}$. $750 / 100 = 7.5\text{ m}$.
Question 8 of 10 Exam Standard
How many seconds are there in 2 hours?
Correct Answer: Option (A)
$1\text{ hour} = 3,600\text{ seconds}$. $2 \times 3,600 = 7,200\text{ seconds}$.
Question 9 of 10 Exam Standard
A sack contains $25\text{ kg } 50\text{ g}$ of flour. What is this in grams?
Correct Answer: Option (A)
$25\text{ kg} = 25,000\text{ g}$. Total = $25,000 + 50 = 25,050\text{ g}$.
Question 10 of 10 Exam Standard
How many cubic centimetres ($\text{cm}^3$) are in 1 litre?
Correct Answer: Option (A)
$1\text{ litre} = 1,000\text{ millilitres} = 1,000\text{ cm}^3$.

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Last-Minute Cadet Revision Matrix

Rapid recall checkpoints to review 24 hours before stepping into the examination hall.

Concept Checkpoint High-Yield Exam Rule & Memory Anchor
Big to Small Multiply when converting from larger to smaller units.
Small to Big Divide when converting from smaller to larger units.
Quintal & Ton 1 Quintal = 100 kg; 1 Metric Ton = 10 Quintals = 1,000 kg.
Area Square Multiplier 1 m² = 10,000 cm² (100 × 100).
Frequently Asked Questions
How many questions from Conversion of Units appear in the AISSEE Class VI exam?
Typically, 2 to 3 questions directly test Conversion of Units in the 50-question Mathematics paper, contributing 6 to 9 marks towards the 150-mark section total.
Is there any negative marking for incorrect answers in AISSEE Class VI?
No. The National Testing Agency (NTA) does not apply negative marking in the AISSEE Class VI entrance examination. Candidates should attempt every single question.
What is the best way to revise Conversion of Units before the exam?
Review the high-yield formulas, practice the 10 interactive drill MCQs on this page, and memorize the revision checkpoints matrix.