Measurements — Class 3 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 3 Mathematics. Standard units for length, weight and capacity, and how to convert between them.

1. Why standard units

You can measure a desk in handspans, but your handspan and your friend's are not the same. The two of you would get different answers for the same desk.

Standard units fix that. A centimetre is the same length for everybody, everywhere, so measurements can be compared and shared.

2. The three families

Choose the unit to suit the thing. A pencil is measured in centimetres, a classroom in metres, the distance to another town in kilometres.

3. Converting units

Each family works in thousands or hundreds, and the numbers are worth learning once.

$1\text{km}=1000\text{m},1\text{m}=100\text{cm}$

$1\text{kg}=1000\text{g},1\text{L}=1000\text{mL}$

To go from the bigger unit to the smaller one, multiply. So 3 km = 3000 m, and 4 kg = 4000 g.

To go from the smaller unit to the bigger one, divide. So 500 cm = 5 m, and 750 g is three quarters of a kilogram.

The word kilo means thousand, and it means the same thing every time it appears. A kilometre is a thousand metres and a kilogram is a thousand grams.

4. Half and quarter measures

Half of a metre is 50 cm, because half of 100 is 50. So 1.5 m is 1 m and 50 cm, not 1 m and 5 cm.

The same reasoning works throughout:

• Half a kilogram = 500 g
• Quarter of a kilogram = 250 g
• Half a litre = 500 mL
• Quarter of a litre = 250 mL

5. Reading the instrument

A ruler starts at 0, not at the edge of the plastic. Line the object up with the 0 mark, or every reading will be too long.

A weighing scale shows kilograms with smaller marks for grams in between. A measuring jug must be stood on a flat surface and read at eye level, because looking down at it makes the level appear higher than it is.

6. Worked examples

Example 1. Convert 5 km to metres.

Bigger unit to smaller, so multiply: 5 × 1000 = 5000 m.

Example 2. Convert 500 cm to metres.

Smaller unit to bigger, so divide: 500 ÷ 100 = 5 m.

Example 3. A bottle holds 1 L. How many 200 mL cups can be filled from it?

1 L is 1000 mL, and 1000 ÷ 200 = 5 cups.

Example 4. Rani buys 2 kg of rice and 500 g of dal. What is the total weight?

Convert to one unit first. 2 kg = 2000 g, and 2000 + 500 = 2500 g, which is 2 kg 500 g.

Adding 2 and 500 straight away would give 502 of nothing at all. Quantities can only be added once they are in the same unit.

7. Practice

1. Convert 3 m to centimetres.
2. Convert 2 L to millilitres.
3. Convert 4000 g to kilograms.
4. Write 1.5 m in metres and centimetres.
5. A jug holds 2 L. How many 250 mL glasses can be filled?
6. A parcel weighs 1 kg 250 g. Write this in grams.
7. Ravi walks 750 m to school and 750 m back. How far does he walk in all, in kilometres?

8. Answers

1. 300 cm.
2. 2000 mL.
3. 4 kg.
4. 1 m 50 cm.
5. 2000 ÷ 250 = 8 glasses.
6. 1250 g.
7. 1500 m, which is 1.5 km.

9. Summary

• Standard units let different people compare the same measurement.
• 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL.
• Bigger unit to smaller: multiply. Smaller to bigger: divide.
• "Kilo" always means a thousand.
• Half a metre is 50 cm, so 1.5 m is 1 m 50 cm.
• Read a ruler from the 0 mark and a jug at eye level.
• Convert to a common unit before adding or subtracting.