Measurements — Exercise Solutions
How to Use This Page
This page provides step-by-step solutions for every exercise in Class 6 Maths: Measurements (Samacheer Kalvi / TN State Board). Work through each problem on your own first, then check your working against the solutions here. Every conversion and calculation is shown with full working — unit conversions, intermediate steps, and final answers with correct units.
Key Concepts (Quick Recap)
Length
Length measures how long or far something is. The SI unit of length is the metre (m).
| From | To | Multiply By |
|---|---|---|
| kilometre (km) | metre (m) | 1000 |
| metre (m) | centimetre (cm) | 100 |
| metre (m) | millimetre (mm) | 1000 |
| centimetre (cm) | millimetre (mm) | 10 |
| kilometre (km) | centimetre (cm) | 1,00,000 |
Key conversions to remember:
- 1 km = 1000 m
- 1 m = 100 cm
- 1 m = 1000 mm
- 1 cm = 10 mm
Mass (Weight)
Mass measures how heavy something is. The SI unit of mass is the kilogram (kg).
| From | To | Multiply By |
|---|---|---|
| kilogram (kg) | gram (g) | 1000 |
| kilogram (kg) | milligram (mg) | 10,00,000 |
| gram (g) | milligram (mg) | 1000 |
| gram (g) | centigram (cg) | 100 |
| kilogram (kg) | centigram (cg) | 1,00,000 |
Key conversions to remember:
- 1 kg = 1000 g
- 1 g = 1000 mg
- 1 g = 100 cg
- 1 kg = 1,00,000 cg
- 1 kg = 10,00,000 mg
Capacity (Volume)
Capacity measures how much liquid a container can hold. The SI unit of capacity is the litre (l).
| From | To | Multiply By |
|---|---|---|
| kilolitre (kl) | litre (l) | 1000 |
| litre (l) | millilitre (ml) | 1000 |
| kilolitre (kl) | millilitre (ml) | 10,00,000 |
Key conversions to remember:
- 1 kl = 1000 l
- 1 l = 1000 ml
- 1 kl = 10,00,000 ml
Time
| From | To | Multiply By |
|---|---|---|
| hour (hr) | minute (min) | 60 |
| minute (min) | second (s) | 60 |
| hour (hr) | second (s) | 3600 |
| day | hour | 24 |
| year | days | 365 (366 in leap year) |
Key conversions to remember:
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 hour = 3600 seconds
- 1 day = 24 hours
- 1 year = 365 days (366 in a leap year)
Fundamental Rules
1. To convert from a larger unit to a smaller unit, multiply. (e.g., km to m: multiply by 1000) 2. To convert from a smaller unit to a larger unit, divide. (e.g., m to km: divide by 1000) 3. Only quantities with the same unit can be added or subtracted. You cannot add 2 m and 5 kg — they measure different physical quantities. 4. Always write the unit with your answer. A number without a unit is incomplete.
Exercise 2.1 — Fundamental Unit Conversions
Converting Between Length Units
Q1. Convert 5 km into metres.
1 km = 1000 m
5 km = 5 x 1000 m = 5000 m
Q2. Convert 3 km 250 m into metres.
3 km = 3 x 1000 = 3000 m
Add the 250 m: 3000 + 250 = 3250 m
Q3. Convert 7500 m into kilometres.
1 km = 1000 m, so 1 m = 1/1000 km
7500 m = 7500 / 1000 = 7.5 km
Q4. Convert 2 m 45 cm into centimetres.
2 m = 2 x 100 = 200 cm
Add the 45 cm: 200 + 45 = 245 cm
Q5. Convert 560 cm into metres.
1 m = 100 cm, so 1 cm = 1/100 m
560 cm = 560 / 100 = 5.6 m
Q6. Convert 3 m 75 cm into centimetres.
3 m = 3 x 100 = 300 cm
Add the 75 cm: 300 + 75 = 375 cm
Converting Between Mass Units
Q7. Convert 4 kg into grams.
1 kg = 1000 g
4 kg = 4 x 1000 = 4000 g
Q8. Convert 2 kg 350 g into grams.
2 kg = 2 x 1000 = 2000 g
Add the 350 g: 2000 + 350 = 2350 g
Q9. Convert 7500 g into kilograms.
1 kg = 1000 g, so 1 g = 1/1000 kg
7500 g = 7500 / 1000 = 7.5 kg
Converting Between Capacity Units
Q10. Convert 5 litres into millilitres.
1 l = 1000 ml
5 l = 5 x 1000 = 5000 ml
Q11. Convert 3 l 450 ml into millilitres.
3 l = 3 x 1000 = 3000 ml
Add the 450 ml: 3000 + 450 = 3450 ml
Q12. Convert 8500 ml into litres.
1 l = 1000 ml, so 1 ml = 1/1000 l
8500 ml = 8500 / 1000 = 8.5 l
Converting Between Time Units
Q13. Convert 3 hours into minutes.
1 hour = 60 minutes
3 hours = 3 x 60 = 180 minutes
Q14. Convert 2 hours 30 minutes into minutes.
2 hours = 2 x 60 = 120 minutes
Add the 30 minutes: 120 + 30 = 150 minutes
Q15. Convert 150 minutes into hours and minutes.
150 / 60 = 2 remainder 30
So 150 minutes = 2 hours 30 minutes
Additional Questions
Q1. Convert 200 mg into grams.
1 g = 1000 mg, so 1 mg = 1/1000 g
200 mg = 200 / 1000 = 0.2 g
Q2(a). State the three fundamental (basic) units in the metric system for length, mass, and capacity.
The metric system is built on three fundamental quantities, each with a base unit:
| Quantity | Fundamental Unit |
|---|---|
| Length | metre (m) |
| Mass (Weight) | gram (g) |
| Capacity (Volume) | litre (l) |
These are the standard units from which all other units (km, kg, ml, etc.) are derived by multiplying or dividing by powers of 10.
Q2(b). A cow gives 10 litres of milk in the morning and 8 litres of milk in the evening. Find the total quantity of milk given by the cow in one week, expressed in millilitres.
Step 1: Find the total milk per day.
Milk per day = 10 l + 8 l = 18 litres
Step 2: Find the total milk for one week (7 days).
Milk per week = 18 l x 7 = 126 litres
Step 3: Convert litres to millilitres.
1 l = 1000 ml
126 l = 126 x 1000 = 1,26,000 ml
Q3. A shop has 20 kg 280 g of sugar. The shopkeeper transfers 2 kg 720 g of sugar into packets seven times. Find the remaining quantity of sugar in centigrams.
Step 1: Convert the total sugar to grams.
20 kg 280 g = (20 x 1000) + 280 = 20,000 + 280 = 20,280 g
Step 2: Convert the transfer amount to grams.
2 kg 720 g = (2 x 1000) + 720 = 2000 + 720 = 2720 g
Step 3: Find the total sugar transferred in 7 packets.
Total transferred = 2720 g x 7 = 19,040 g
Step 4: Find the remaining sugar in grams.
Remaining = 20,280 g - 19,040 g = 1240 g
Step 5: Convert grams to centigrams.
1 g = 100 cg
1240 g = 1240 x 100 = 1,24,000 cg
Q4. 1 m 20 cm of cloth is needed to stitch one blouse. How much cloth is needed to stitch 20 such blouses, expressed in centimetres?
Step 1: Convert the cloth per blouse to centimetres.
1 m 20 cm = (1 x 100) + 20 = 100 + 20 = 120 cm
Step 2: Multiply by the number of blouses.
Cloth for 20 blouses = 120 cm x 20 = 2400 cm
Q5. Can you add 2 m 20 cm and 4 kg 80 g? Give reasons.
2 m 20 cm is a measurement of length.
4 kg 80 g is a measurement of mass (weight).
These two quantities measure different physical quantities. Addition is meaningful only when the quantities have the same physical nature. You cannot add length and mass, just as you cannot add distance and weight.
Q6. 150 ml of juice is distributed to each person. If 200 people are present, how many litres of juice are needed?
Step 1: Find the total juice in millilitres.
Total juice = 150 ml x 200 = 30,000 ml
Step 2: Convert millilitres to litres.
1 l = 1000 ml, so 1 ml = 1/1000 l
30,000 ml = 30,000 / 1000 = 30 litres
Q7. 1920 kg of fertiliser is required for 120 trees. Find the quantity of fertiliser required per tree.
Step 1: Divide the total fertiliser by the number of trees.
Fertiliser per tree = 1920 kg / 120 = 16 kg
Q8. Convert 7 kg 250 g into: (i) grams (ii) milligrams (iii) centigrams
Step 1: Convert to grams.
7 kg 250 g = (7 x 1000) + 250 = 7000 + 250 = 7250 g
(i) Answer: 7250 g
Step 2: Convert grams to milligrams.
1 g = 1000 mg
7250 g = 7250 x 1000 = 72,50,000 mg
(ii) Answer: 72,50,000 mg
Step 3: Convert grams to centigrams.
1 g = 100 cg
7250 g = 7250 x 100 = 7,25,000 cg
(iii) Answer: 7,25,000 cg
Q9. Convert 20 m 20 cm into: (i) centimetres (ii) metres (decimal) (iii) kilometres (decimal)
(i) Convert to centimetres:
20 m 20 cm = (20 x 100) + 20 = 2000 + 20 = 2020 cm
Answer (i): 2020 cm
(ii) Convert to metres (decimal form):
20 m 20 cm = 20 m + (20/100) m = 20 m + 0.20 m = 20.20 m
Answer (ii): 20.20 m
(iii) Convert to kilometres (decimal form):
1 km = 1000 m, so 1 m = 1/1000 km
20.20 m = 20.20 / 1000 = 0.02020 km
Answer (iii): 0.02020 km
Q10. Convert 85 l 720 ml into: (i) millilitres (ii) litres (decimal) (iii) kilolitres (decimal)
(i) Convert to millilitres:
85 l = 85 x 1000 = 85,000 ml
Add 720 ml: 85,000 + 720 = 85,720 ml
Answer (i): 85,720 ml
(ii) Convert to litres (decimal form):
85 l 720 ml = 85 l + (720/1000) l = 85 l + 0.72 l = 85.72 l
Answer (ii): 85.72 l
(iii) Convert to kilolitres (decimal form):
1 kl = 1000 l, so 1 l = 1/1000 kl
85.72 l = 85.72 / 1000 = 0.08572 kl
Answer (iii): 0.08572 kl
Q11. Which is the greatest among: 0.007 g, 0.7 kg, 70 mg?
Step 1: Convert all to the same unit (grams).
0.007 g is already in grams: 0.007 g
0.7 kg: 1 kg = 1000 g, so 0.7 kg = 0.7 x 1000 = 700 g
70 mg: 1 g = 1000 mg, so 70 mg = 70/1000 = 0.07 g
Step 2: Compare the values in grams.
| Value | In grams |
|---|---|
| 0.007 g | 0.007 g |
| 0.7 kg | 700 g |
| 70 mg | 0.07 g |
Clearly, 700 g > 0.07 g > 0.007 g.
Q12. A bus leaves Chennai at 4:30 p.m. and reaches Trichy at 5:55 p.m. How long does the journey take?
Step 1: Note the start and end times.
Start time = 4:30 p.m.
End time = 5:55 p.m.
Step 2: Subtract start time from end time.
From 4:30 p.m. to 5:30 p.m. = 1 hour
From 5:30 p.m. to 5:55 p.m. = 25 minutes
Total time = 1 hour 25 minutes
Verification: 4:30 + 1 hr 25 min = 4:30 + 1:25 = 5:55 p.m.
Q13. A film starts at 6:30 p.m. and its duration is 3 hours 15 minutes. At what time does the film end?
Step 1: Add the duration to the start time.
Start time = 6:30 p.m.
Duration = 3 hours 15 minutes
Step 2: Add the hours.
6:30 + 3 hours = 9:30 p.m.
Step 3: Add the minutes.
9:30 + 15 minutes = 9:45 p.m.
Q14. A train arrives at Chennai at 11:55 a.m. It was late by 1 hour 25 minutes. What was the scheduled arrival time?
Step 1: Note the actual arrival time and the delay.
Actual arrival = 11:55 a.m.
Delay = 1 hour 25 minutes
Step 2: Subtract the delay from the actual arrival to find the scheduled time.
From 11:55 a.m., go back 1 hour: 10:55 a.m.
From 10:55 a.m., go back 25 minutes: 10:30 a.m.
Verification: Scheduled time + delay = 10:30 a.m. + 1 hr 25 min = 11:55 a.m.
Q15. A fashion show starts at 8:45 p.m. and Kavitha stays for 2 hours 30 minutes. At what time does she leave?
Step 1: Add the duration to the start time.
Start time = 8:45 p.m.
Duration = 2 hours 30 minutes
Step 2: Add the hours.
8:45 + 2 hours = 10:45 p.m.
Step 3: Add the minutes.
10:45 + 30 minutes = 11:15 p.m.
Q16. A man travels by bus for 4 hours 45 minutes and then by train for 4 hours 45 minutes. Find the total travel time.
Step 1: Add the two time durations.
Bus travel = 4 hr 45 min
Train travel = 4 hr 45 min
Step 2: Add the hours.
4 + 4 = 8 hours
Step 3: Add the minutes.
45 + 45 = 90 minutes
Step 4: Convert 90 minutes to hours and minutes.
90 minutes = 1 hour 30 minutes
Step 5: Add to the hours.
8 hours + 1 hour 30 minutes = 9 hours 30 minutes
Q17. Ramu left home at 4:30 p.m. to play and returned after 3 hours 25 minutes. At what time did he return?
Step 1: Note the start time and duration.
Start time = 4:30 p.m.
Duration = 3 hours 25 minutes
Step 2: Add the hours.
4:30 + 3 hours = 7:30 p.m.
Step 3: Add the minutes.
7:30 + 25 minutes = 7:55 p.m.
Q18. School starts at 7:30 a.m. and ends at 12:45 p.m. How long is the school day?
Step 1: Note the start and end times.
Start time = 7:30 a.m.
End time = 12:45 p.m.
Step 2: Find the difference.
From 7:30 a.m. to 12:30 p.m. = 5 hours
From 12:30 p.m. to 12:45 p.m. = 15 minutes
Total = 5 hours 15 minutes
Verification: 7:30 + 5 hr 15 min = 12:45 p.m.
Q19. Date of birth is 25.07.2000. Find the age on 29.08.2017.
Step 1: Note the two dates.
Date of birth = 25 July 2000
Age on = 29 August 2017
Step 2: Calculate the years.
2017 - 2000 = 17 years
Step 3: Calculate the months and days.
From 25 July to 29 August:
- From 25 July to 25 August = 1 month
- From 25 August to 29 August = 4 days
So the full age is 17 years, 1 month, and 4 days.
Q20. Which of the following are leap years? 2000, 2018, 2012
A year is a leap year if it is divisible by 4. However, century years (like 1900, 2000) must be divisible by 400 to be leap years.
2000: 2000 / 400 = 5 (exactly divisible). So 2000 is a leap year.
2018: 2018 / 4 = 504.5 (not exactly divisible). So 2018 is not a leap year.
2012: 2012 / 4 = 503 (exactly divisible). So 2012 is a leap year.
| Year | Divisible by 4? | Divisible by 400? | Leap Year? |
|---|---|---|---|
| 2000 | Yes | Yes | Yes |
| 2018 | No | -- | No |
| 2012 | Yes | -- | Yes |
Q21. Convert the following to railway (24-hour) time:
(i) 12:05 a.m.
(ii) 4:20 p.m.
Rule for 24-hour time:
- For a.m. times: the 24-hour time is the same as the 12-hour time, except that 12:xx a.m. becomes 00:xx hrs.
- For p.m. times: add 12 to the hour (except 12:xx p.m. stays as 12:xx).
(i) 12:05 a.m.
12:xx a.m. corresponds to 00:xx in 24-hour time.
12:05 a.m. = 00:05 hrs
(ii) 4:20 p.m.
Add 12 to the hour: 4 + 12 = 16
4:20 p.m. = 16:20 hrs
Common Mistakes
1. Mixing units in addition or subtraction: You cannot add 2 m 20 cm and 4 kg 80 g because they are different physical quantities (length vs. mass). Always confirm the quantities are of the same type before adding or subtracting.
2. Confusing multiply vs. divide in conversions: To go from a larger unit to a smaller unit (km to m), you multiply. To go from a smaller unit to a larger unit (m to km), you divide. Getting this backwards is the most common error.
3. Forgetting to convert compound quantities: In a sum like "5 km 250 m + 3 km 750 m", many students add the km and m separately and get the right answer, but forget to carry over when m exceeds 1000. Always convert to a single unit first if unsure.
4. Omitting units in the final answer: Writing just "5000" instead of "5000 m" loses marks. Every measurement answer must include the correct unit.
5. Time subtraction errors when borrowing: When subtracting times like 5:55 p.m. minus 4:30 p.m., some students subtract correctly, but get confused when the minute subtrahend is larger (e.g., 2:15 p.m. minus 10:45 a.m.). Remember: borrow 1 hour (= 60 minutes) when needed.
6. Misunderstanding leap year rules for century years: A century year must be divisible by 400, not just 4. So 2000 is a leap year but 1900 is not.
7. Confusing a.m. and p.m. in 24-hour conversion: 12:xx a.m. converts to 00:xx hrs, not 12:xx hrs. Similarly, 12:xx p.m. stays as 12:xx hrs in 24-hour format. Students often mix these up.
Exam Checklist
Before your exam, make sure you can:
- [ ] Convert between km, m, cm, and mm (length)
- [ ] Convert between kg, g, mg, and cg (mass)
- [ ] Convert between kl, l, and ml (capacity)
- [ ] Convert between hr, min, and s (time)
- [ ] Add and subtract compound quantities (e.g., 5 km 250 m + 3 km 750 m)
- [ ] Compare quantities by converting to the same unit first (e.g., which is greater: 0.007 g, 0.7 kg, or 70 mg?)
- [ ] Solve word problems involving daily-life contexts (cloth, milk, fertiliser, travel time)
- [ ] Calculate elapsed time (start time to end time)
- [ ] Work backwards from a late arrival to find the scheduled time
- [ ] Convert 12-hour (a.m./p.m.) time to 24-hour (railway) time and vice versa
- [ ] Determine whether a given year is a leap year
- [ ] Calculate age given date of birth and current date
- [ ] Remember the rule: only quantities of the same kind can be added or compared
- [ ] Always write the unit with every answer