Table of contents |
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Introduction |
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What is Measurement? |
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1. Length |
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2. Mass (Weight) |
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3.Capacity |
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Decimals and Measurements |
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Basic Operations on Measurements |
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Finding Fractions of Quantities |
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Imagine you are going on an adventure! ️To make it a success, you’ll need to measure a lot of things
That’s exactly what we will learn in this chapter – Measurement!
Measurement means determining the size, length, capacity, weight, or time of something using standard units.
Length tells us how long or tall something is.
Follow the diagram to do the conversions
Examples including conversions are given below
Example 1: Convert 3 km into meter.
Sol: We know that 1 km = 1000 m
hence, 3 km = 3 x 1000
= (3 × 1000) m
= 3000 m
Example 2: Convert 370 m into hectometer.
Sol: We know that 1 Hectometer (hm) = 100 m
(i) 1001 m = 1 hm
(ii) 1100 m = 1 hm
(iii) 370 m = 370 × 1100 hm = 370100 hm = 3.7 hm
Example 3: Convert 2000 mm into meter.
Sol: As We know that: 1 mm = 11000 meters = 0.001m
So, 2000 mm = 20001000 meters = 2 meters.
Example 4: Convert 12000 cm to dam.
Sol: 1 cm = 11000 dam
=Therefore 12000 cm = 120001000 dam
= 12 dam
Mass tells us how heavy an object is.
Follow the diagram to do the conversions
Example 1: Conversion of various units to grams and vice versa.
(i) 24 kg = (24 × 1000) g = 24000 g
(ii) 1.217 g = (1.217 × 1000) mg = 1217 mg
(iii) 3200 mg = (3200 ÷ 1000) g = 3.2 g
(iv) 315 cg = (315 ÷ 100) g = 3.15 g
Example 2: Conversion between Units
(i) 14 mg = (14 ÷ 10) cg = 1.4 cg(ii) 300 dg = (300 ÷ 100) dag = 3 dag
(iii) 2417 cg = (2417 ÷ 1000) dag = 2.417 dag
(iv) 38 kg = (38 × 100) dag = 3800 dag
(v) 23.7 dg = (23.7 × 10) cg = 237 cg
(vi) 4 hg = (4 × 1000) dg = 4000 dg
Example 3: A basket of apples weighs 2.5 kg. How much is that in g?
Sol: 2.5 × 1000 = 2500 g
The basket of apples weighs 2500 g.
Capacity tells us how much a container can hold (liquid).
Follow the diagram to do the conversions
Examples of the conversions are given below
Example 1: Conversion of various units to litres and litres to various units
(i) 2.3 kL = (2.3 × 1000) L = 2300 L
(ii) 1.8 cL = (1.8 ÷ 100) L = 0.018 L
(iii) 64 hL = (64 × 100) L = 6400 L
(iv) 600 L = (600 ÷ 100) hL = 6 hL
(v) 7315 mL = (7315 ÷ 1000) L = 7.315 L
(vi) 11.9 L = (11.9 × 1000) mL = 11900 mL
Example 2: Conversions between Units.
(i) 25 hL = (25 × 10) daL = 250 daL
(ii) 13.8 dL = (13.8 × 100) mL = 1380 mL
(iii) 500 daL = (500 ÷ 100) kL = 5 kL
(iv) 3.117 hL = (3.117 × 1000) dL = 3117 dL
Example: Convert 5.45 meters into centimetres.
Sol: 1meter=100 centimeters
5.45 × 100 = 545 centimeters
Example: Convert 2.85 kilograms into grams.
Sol:
1 kilogram = 1000 grams
2.85 Kg = 2.85 × 1000=2850 gram
Example: Convert 3.5 litres into millilitres.
Sol: As we know,
=> 1 litre =1000 millilitres
=> 3.5×1000 = 3500 millilitres
=> 3500 milliliters
Sol: Length of the line segment in the beginning = 15 cm 4 mm
Length of line segment left after erasing = 7 cm 6 mm
Length of line segment erased = 15 cm 4 mm – 7 cm 6 mm
= 7 cm 8 m m
= 7 + 810 cm = 7.8 cm.
Example 2: Add 3 cm 4 mm and 9 cm 8 mm.
Sol:
12 mm
= 10 mm + 2 mm
= 1 cm + 2 mm
= 13 cm 2 mm = 13.2 cm.
Example 3: Subtract 8 kL 150 L – 4 kL 850 L.
Sol:
150 L < 850 L
Borrow 1 kL = 1000 L
1000 L + 150 L
= 1150 L
= 3.300 kL.
Example 1: Find the height of a pile of 25 books, if each book is 3 cm, 5 mm thick (in centimetres).
Sol: Thickness of 1 book = 3 cm 5 mm = 3.5 cm
Height of 25 books = 3.5 cm × 25
= 87.5 cm
Thus, height of the pile of 25 books
= 87.5 cm.
Example 2: A carton full of fruits weighs 6 kg 125 g. What is the weight of 12 such cartons in kg?
Sol: Weight of one carton = 6 kg 125 g
= 6.125 kg
∴ Weight of 12 cartons = (6.125 × 12) kg
= 73.500 kg
= 73 kg 500 g.
Example 1: Reena prepared 4 L 156 mL of orange juice. Distribute it equally among 8 children. How many mL of orange juice each child gets?
Sol: Juice Reena prepared = 4 L 156 mL = 4.156 L
When distributed among 8 children,
juice each child gets = (4.156 ÷ 8) L
= 0.51 95 L
= 519 .5 mL.
Example 2: How many 150 mL glasses can I fill with 5 bottles of soft drinks each holding 1.2 litres?
Sol: Total soft drink in 5 bottles = 1.2 L × 5 = 6.0 = 6 L
∵ 1 L = 1000 mL
Total soft drink = 6 L = 6 × 1000 = 6000 mL
Number of 150 mL of glasses that can be filled = 6000 mL ÷ 150 mL = 40
Thus, with 6 L of soft drink, I can fill 40 glasses of 150 mL.
Example 1: A basket contains 3 kg 705 g of mangoes. 23 of the mangoes are eaten by Mr Bhasin. Lata, his daughter, gets 25 of the remaining mangoes. What is her share in grams?
Sol: Total weight of mangoes = 3 kg 705 g
Mangoes eaten by Mr Bhasin
= 23 of 3 kg 705 g= 23 of 3.705 g
= 23 x 3.705 g
= 2 x 3.7053 kg
= 7.413 kg = 2.47 kg
Mangoes left = 3.705 kg – 2.47 kg
= 1.235 kg
Mangoes eaten by Lata
= (0.494 × 1000) g
= 494 g
So, Lata ate 494 g of the mangoes.
Example 2: Anshul had 45 kg of wafers. He packed all the wafers equally into 5 small packets. How many grams of wafers were there in each packet?
Sol: Total wafers with Anshul = 45 kg
= 45 x 1000 g
= 800 g
800 g wafers are filled in 5 small packets.
∴ Wafers in one packet = 800 ÷ 5
= 8005 = 160 g
So, each packet contains 160 g of wafers.
Example 3: Madhuri drew a line segment of length 20 cm 5 mm. She accidentally erased 2 / 5 of it. What is the length of the remaining line segment in cm?
Sol: Length of the line segment drawn = 20 cm 5 mm = 20.5 cm
Length of the erased line segment = 25 of 20.5 cm
= (2 × 4.1) cm
= 8.2 cm
Length of the remaining line segment = 20.5 cm – 8.2 cm
= 12.3 cm.
56 videos|223 docs|40 tests
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1. What is the difference between length and mass? | ![]() |
2. How do you convert between different units of length? | ![]() |
3. What are some common units of capacity and how are they related? | ![]() |
4. How do decimals relate to measurements? | ![]() |
5. How can I find a fraction of a quantity in measurements? | ![]() |