Measurement

Measurement
In the previous class, we have studied that the basic units of measuring length, weight and capacity are metre (m), gram (g) and litre (l) respectively. In this class, we will study more about the units of measurement.

Measurement of Length

Metre is the basic unit of measuring length. The units smaller than the basic unit are named by adding prefixes dedi, centi, milli and so on while the units bigger than the basic unit are named by adding prefixes deca, hecto, kilo and so on before the basic unit.

Look at the table given below

From the above table, it is clear that each bigger unit is 10 times of its smaller unit and each smaller unit is \(1 \over 10\) times of its bigger unit, So, we have

1 km = 1000 m

1 hm = 100 m

 1 dam = 10 m

1 dm =\(1 \over 10\) m = 0.1 m

 1 cm = \(1 \over 100 \)m = 0.01 m

 1 mm = \(1\over 1000 \)m = 0.001 m

Example:

Example: Convert the following into metres :

(a)3.8 km  (b) 40 cm (c) 25 dm

Solution:

 (a) ∵ 1 km = 1000 m

∴ 3.8 km = 3.8 × 1000 m = 3800 m

(b)∵ 1 cm =\(1 \over 100\) m

∴ 40 cm = 40 × m = 0.4 m

(c)∵ 1 dm = \(1\over 10\) m

∴ 25 dm = 25 × m = 2.5

Example: Convert the following :

(a) 5 km 3 m 6 cm into m            (b) 4 m 40 cm 4 mm into cm

Solution:

(a)∵ 1 km = 1000 m and 1 cm =\(1\over 100\) m

∴ 5 km 3 m 6 cm = 5 km + 3 m + 6 cm

= (5 × 1000) m + 3 m +\(\left( 6\times \frac{1}{100} \right)\)

= 5000 m + 3 m + 0.06 m

 = 5003.06 m

(b)∵ 1 m = 100 cm and 1 mm =\(1 \over 10\) cm

∴ 4 m 40 cm 4 mm = 4 m + 40 cm + 4 mm

= (4 × 100) cm + 40 cm +

= 400 cm + 40 cm + 0.4 cm

= 440.4 cm

Measurement

Measurement of Weight

Gram is the basic unit of measuring weight. The units smaller than the basic unit are named by adding prefixes deci, centi, milli and so on while the units bigger than the basic unit are named by adding prefixes deca, hecto, kilo and so on before the basic unit.

Look at the table below:

From the above table, it is clear that each bigger unit is 10 times of its smaller unit and each smaller unit is \(1 \over 10 \)times of its bigger unit. 50, we have

1 kg = 1000 g

 1 hg = 100 g

1 dag = 10 g

1 dg = \(1 \over 10\)g = 0.1 g

1 cg =\(1\over 100\) g = 0.01 g

1 mg =\(1 \over 1000 \) g = 0.001 g

Example: Convert the following into grams :

(a) 8.3 kg          (b) 15 dg          (c) 130 mg

Solution:    (a) ∵ 1 kg = 1000 m

∴ 8.3 kg = 8.3 ×1000g=8300g

(b)1 dg = g

∴ 15 dg = 15 ×\(1 \over10\) g = 1.5g

(c)1 mg = \(1 \over1000\) g

∴ 130 mg = 130 × \(1\over 1000\)g = 0.13 g

Example: Convert the following:

(a) 3 hg 2 dag into g               (d) 30 g 50 mg into cg

Solution: (a) ∵ 1 hg = 100 g and 1 dag = 10 g

∴ 3 hg 2 dag = 3 hg + 2 dag

= (3 × 100) g + (2 × 10) g

= 300 g + 20 g

= 320 g

(b) ∵ 1 g = 100 cg and 1 mg = cg

30 g 50 mg = 30 g + 50 mg

= (30 × 100) cg + \(\left( 50\times \frac{1}{10} \right)\) × cg

= 3000 cg + 5 cg

= 3005 cg

Measurement

Measurement of Capacity

Litre is the basic unit of measuring capacity. The units smaller than the basic unit are named by adding prefixes deci, centi, milli and so on while the units bigger than the basic unit are named by adding prefixes deca, hecto, kilo and so on before the basic unit.

Look at the table below:

From the above table, it is clear that each bigger unit is 10 times of its smaller unit and each smaller unit is times of its bigger unit. So, we have

1 kl = 1000 l

1 hl = 100 l

1 dal = 10 l

1 dl =\(1 \over 10\) l = 0.1 l

1 cl =\(1 \over 100\) l = 0.01 l

1 ml =\(1\over 1000\) l = 0.001 l

Example: Convert the following into litres :

(a) 2.5 kl         (b) 50 dl                (c) 250 ml

Solution:

(a)∵ 1 kl = 1000 l

∴ 2.5 kl = 2.5 × 1000 l = 2500 l

(b)∵ 1 dl =\(1 \over 10\) l

∴ 50 dl = 50 × l = 5 l

©∵ 1 ml =\(1\over 1000\)l

∴ 250 ml = 250 × l = 0.25 l

Example: Convert the following

(a) 4 kl 3 hl 2 dal 1 l into l                (b) 2.5 hl 2 l 30 dl into l

Solution: (a) ∵ 1 kl = 1000 l, 1 hl = 100 l and 1 dal = 10 l

∴ 4 kl 3 hl 2 dal 1 l = 4 kl + 3 hl + 2 dal + 1 l

= (4 × 1000) l + 3 (3 × 100) l + (2 × 10) l + 1 l

= 4000 l + 300 l + 20 l + 1 l

= 4321l

(b) ∵ 2.5 hl = 2 l and 30 dl =\(1 \over 10\)l

∴ 2.5 hl 2 l 30 dl = 2.5 hl + 2 l + 30 dl

= (2.5 × 100) l + 2 l + \(\left( 30\times \frac{1}{10} \right)\)l

= 250 l + 2 l + 3 l

= 255 l

Measurement

Fundamental Operations on Measurement

Example: Mohan covered a distance of 15 km 275 m in the first hour and 18 km 803 m in the second hour. What distance did he cover in two hours?

Solution: Distance covered in first hour = 15 km 275 m

Distance covered in second hour = 18 km 803 m

Total distance covered in two hours = 15 km 275 m + 18 km 803 m

= 34 km 78 m

So, he covered 34 km 78 m in two hours.

Example: Two containers weigh 1980 g and 2 kg 300 g respectively. Which container is heavy and by how much?

Solution: Weight of first container = 1980 g = 1 kg 980 g

∴ 2 kg 300 g > 1 kg 980 g

∵ Second container is more heavy.

Difference = 2 kg 300 g - 1 kg 980 g = 320 g

So, second container is heavy by 320 g

Example: A pack of juice weighs 7 kg 325 g. What is the weight of 12 such packs in kg?

Solution: Weight of 1 pack of juice = 7 kg 325 g

= 7.325 kg

Weight of 12 packs of juice = 7.325 kg × 12

= 34 kg 78 g

50, the weight of 12 packs of juice is 87.900 kg

Example: A bottle holds 1l 140 ml of shampoo. If Radhika uses 95 ml of shampoo every week, for how many weeks will the bottle of shampoo last?

Solution: Capacity of a bottle of shampoo = 1l 140 ml

Capacity of shampoo used in a week = 95 ml = 1140 ml

Number of weeks, the bottle will last = 1140 ml ÷ 95 ml = 12

 So, the bottle of shampoo will last for 12 weeks.