Measurements — Class 5 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 5 Mathematics, Unit 4. Length, conversion of units, and the four operations on measurements. Taught in August.
1. Choosing the right unit
Banu wants to measure three things: the length of her table, her own height, and the distance from her home to school. They are wildly different sizes, so they need different units.
Metric measurements are used for length and distance.
| Unit | Use it for | Relationship |
|---|---|---|
| Millimetre (mm) | Very small things — the thickness of a card | 10 mm = 1 cm |
| Centimetre (cm) | A notebook, your height, a geometry box | 100 cm = 1 m |
| Metre (m) | A house, a playground | 1000 m = 1 km |
| Kilometre (km) | The distance between two cities | — |
A signboard reading Chennai 170 km, Trichy 100 km, Madurai 210 km uses kilometres, because metres would give impossibly long numbers.
2. Converting between units
There is one rule, and it never changes.
Big unit into small unit: multiply. Small unit into big unit: divide.
Into millimetres (multiply by 10): 70 cm = 70 × 10 = 700 mm
Into centimetres (multiply metres by 100, or divide millimetres by 10):
- 5 m = 5 × 100 = 500 cm
- 7 m 40 cm = (7 × 100) + 40 = 700 + 40 = 740 cm
- 110 mm = 110 ÷ 10 = 11 cm
Into metres (divide centimetres by 100): 650 cm = 6 m 50 cm
Into kilometres (divide metres by 1000):
- 9000 m = 9000 ÷ 1000 = 9 km
- 2300 m = 2 km 300 m
3. Adding measurements
Write metres under metres and centimetres under centimetres, then add each column. Carry 1 m whenever the centimetres reach 100.
Three ropes measure 1 m 20 cm, 2 m 15 cm and 1 m 25 cm.
| m | cm | |
|---|---|---|
| First rope | 1 | 20 |
| Second rope | 2 | 15 |
| Third rope | + 1 | 25 |
| Total | 4 | 60 |
The total length is 4 m 60 cm.
4. Subtracting measurements
Same columns, and borrow 1 m as 100 cm when the top centimetres are too small.
Kannan bought 90 m 80 cm of cloth and used 43 m 75 cm to stitch uniforms.
90 m 80 cm − 43 m 75 cm = 47 m 5 cm
Here no borrowing was needed, since 80 is larger than 75. Write the answer as 47 m 05 cm to keep the two-digit form.
5. Multiplying measurements
Multiply the metres and the centimetres separately, then tidy up any centimetres over 99.
One ribbon is 4 m 25 cm long. How long are three such ribbons?
4 m 25 cm × 3 = 12 m 75 cm
The centimetres gave 25 × 3 = 75, which is under 100, so nothing carries. The answer is 12 m 75 cm.
6. Dividing measurements
Divide the metres first, then carry any remainder into the centimetres.
84 m 40 cm ÷ 4 = 21 m 10 cm
Check by multiplying back: 21 m 10 cm × 4 = 84 m 40 cm.
7. Distance problems
An odometer is the meter in a vehicle that records the total distance travelled.
Saravanan drives from Puducherry to Chennai, a distance of 165 km. His odometer read 000157 km when he set out. What will it read on arrival?
157 + 165 = 322 km
8. Weight
Weight is measured in grams and kilograms, and the full family of units steps up in tens.
| Conversion |
|---|
| 10 milligram (mg) = 1 centigram (cg) |
| 10 centigram = 1 decigram |
| 10 decigram = 1 gram (g) |
| 1000 gram = 1 kilogram (kg) |
In ordinary work only the last line matters: 1 kg = 1000 g. Everything else follows from it. Half a kilogram is 500 g, a quarter is 250 g, and three quarters is 750 g.
All four operations work on weight, provided the kilogram and gram columns are kept apart and you carry in thousands rather than in tens.
Add 2 kg 450 g and 1 kg 700 g. The grams give 450 + 700 = 1150 g, which is 1 kg and 150 g. Carry that kilogram across: 2 + 1 + 1 = 4 kg. The answer is 4 kg 150 g.
Multiply 3 kg 250 g by 4. The grams give 250 × 4 = 1000 g, exactly 1 kg, and the kilograms give 3 × 4 = 12 kg. Together that is 13 kg.
9. Capacity
Capacity is how much a container holds, and it is measured in millilitres and litres.
| Conversion |
|---|
| 10 millilitre (ml) = 1 centilitre (cl) |
| 10 centilitre = 1 decilitre |
| 10 decilitre = 1 litre (l) |
| 1000 litre = 1 kilolitre (kl) |
The line worth memorising is 1 l = 1000 ml. So half a litre is 500 ml, a quarter is 250 ml and three quarters is 750 ml. That is the same set of numbers as for weight, because both families step in thousands at the point we use them.
Multiply 4 l 200 ml by 3. The millilitres give 200 × 3 = 600 ml and the litres give 4 × 3 = 12 l, so the answer is 12 l 600 ml.
Divide 2 l 320 ml by 2. Half of 2 l is 1 l and half of 320 ml is 160 ml, giving 1 l 160 ml. When the litres do not halve evenly, turn the odd litre into 1000 ml and carry it into the millilitre column before dividing.
10. Worked examples
Example 1. Convert 7 m 5 cm into centimetres.
Solution: (7 × 100) + 5 = 700 + 5 = 705 cm.
Example 2. Convert 505 mm into centimetres and millimetres.
Solution: 505 ÷ 10 = 50 with 5 left over, so 50 cm 5 mm.
Example 3. Convert 326 m into centimetres.
Solution: 326 × 100 = 32,600 cm.
Example 4. Convert 5 km 30 m into metres.
Solution: (5 × 1000) + 30 = 5000 + 30 = 5030 m.
Example 5. True or false: 7000 m is 7 km.
Solution: True, since 1000 m = 1 km.
Example 6. True or false: 400 cm is 4 km.
Solution: False. 400 cm is 4 m. A kilometre is far larger.
Example 7. Add 12 m 45 cm and 8 m 70 cm.
Solution: 45 + 70 = 115 cm = 1 m 15 cm. Carry the metre: 12 + 8 + 1 = 21 m. Answer 21 m 15 cm.
Example 8. A rope 5 m 60 cm long is cut into 4 equal pieces. How long is each?
Solution: 5 m 60 cm = 560 cm. 560 ÷ 4 = 140 cm = 1 m 40 cm.
11. Practice
- How many millimetres make one centimetre?
- Convert 8 m into centimetres.
- Convert 80 mm into centimetres.
- Convert 7500 m into kilometres and metres.
- True or false: 770 mm is 77 cm.
- Add 4 m 75 cm and 3 m 18 cm.
- Subtract 36 m 24 cm from 63 m 47 cm.
- Multiply 2 m 30 cm by 4.
- Divide 96 m 60 cm by 3.
- A car's odometer reads 004520 km before a 180 km journey. What will it read after?
- Add 3 kg 600 g and 2 kg 750 g.
- Multiply 2 l 150 ml by 4.
- Divide 5 kg 500 g by 5.
- How many 250 ml glasses can be filled from 2 litres?
12. Answers
- 10 mm.
- 8 × 100 = 800 cm.
- 80 ÷ 10 = 8 cm.
- 7 km 500 m.
- True, since 770 ÷ 10 = 77.
- 75 + 18 = 93 cm; 4 + 3 = 7 m. Answer 7 m 93 cm.
- 47 − 24 = 23 cm; 63 − 36 = 27 m. Answer 27 m 23 cm.
- 2 m 30 cm × 4 = 9 m 20 cm, since 30 × 4 = 120 cm = 1 m 20 cm and 2 × 4 + 1 = 9 m.
- 96 ÷ 3 = 32 m and 60 ÷ 3 = 20 cm, so 32 m 20 cm.
- 4520 + 180 = 4700 km.
- Grams: 600 + 750 = 1350 g, which is 1 kg 350 g. Kilograms: 3 + 2 + 1 = 6 kg. The answer is 6 kg 350 g.
- 150 × 4 = 600 ml and 2 × 4 = 8 l, so the answer is 8 l 600 ml.
- 5 kg ÷ 5 = 1 kg and 500 g ÷ 5 = 100 g, so the answer is 1 kg 100 g.
- 2 l = 2000 ml, and 2000 ÷ 250 = 8 glasses.
13. Summary
- 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
- Big unit into small unit, multiply; small unit into big unit, divide.
- 7 m 40 cm = 740 cm; 2300 m = 2 km 300 m; 110 mm = 11 cm.
- Add and subtract in two columns, carrying or borrowing 100 cm as 1 m.
- Multiply each part separately, then convert any centimetres over 99 into metres.
- Divide the metres first and carry the remainder into the centimetres.
- An odometer records total distance travelled, so add the journey to the starting reading.
