Length

In this chapter, we deal with the fascinating topic of length. Enjoy the process of comparing different lengths and applying this understanding to the real world. Embrace our newfound knowledge and continue to explore the world of measurement!

Length

Length is a physical measurement that describes how long or short an object is. It helps us compare and describe the size of different objects. It is a fundamental aspect of understanding the physical world around us. Nearly everything in our surroundings such as Laptops, vans, books, pencils, pens, kites, etc. have a certain length.

Different measuring instruments are used to measure length such as measuring tape, measuring rulers, measuring hands (using hand span), measuring sticks, etc. These tools are used to measure the length of objects by comparing the length of objects with the length of the tool itself.

Units of Length

In the world of measurement, we use different units to express length. These units help us describe how long or short objects are.

For example, the height of a rabbit is 90 centimetres (cm) which is the unit we use to measure the length/height.

Metric Units of Length

Metric units of length are a standardized system for measuring the lengths and dimensions of many objects around the world. 

The primary metric units of length are as follows:

1. Millimetre (mm)
2. Centimetre (cm)
3. Decimetre (dm)
4. Metre (m)
5. Decametre (dam)
6. Hectometre (hm)
7. Kilometre (km)

Non Metric Units of Length

Non-metric units of length are not based on the metres as a standard of measurement.

The primary non-metric units of length are as follows:

1. Inches (in)
2. Foot (ft)

Conversions of Units of Length

To convert from a smaller unit to a larger unit of length, you multiply the value related to the smaller unit of length by 10./p>

Conversely, to convert from a larger unit to a smaller unit of length, you divide the value related to the larger unit of length by 10.

Metric units are based on powers of ten which makes them easy to convert and work with. This conversion of one unit to another is shown as:

Here are various common metric units of length and their conversion relationships are as follows:

Kilometres (km) to metres (m):

→ 1 km = 1000 m
→ To convert from km to m, multiply by 1000.
→ Example: 1.7 km = 1.7 × 1000 = 1700 m

Metres (m) to kilometres (km):

→ 1 m = 1/1000 km = 0.001 km
→ To convert from m to km, divide by 1000 or multiply by 0.001.
→ Example: 9000 m = 9000÷1000 = 9 km

Or

9000 m = 9000 × 0.001 km
             = 9000 ×1/1000km
              = 9 km

Metres (m) to millimetres (mm):

→ 1 m = 1000 mm
→ To convert from m to mm, multiply by 1000.
→ Example: 11 m = 11 × 1000 = 11000 mm

Millimetres (mm) to Metres (m):

→ 1 mm = 1/1000 m = 0.001 m
→ To convert from mm to cm, divide by 1000.
→ Example: 7000 mm = 7000 / 1000 = 7 m

Or

7000 mm = 7000 × 0.001 m
                = 7000 ×1/1000m 
                 = 7 m

Metres (m) to centimetres (cm):

→ 1 m = 100 cm
→ To convert from m to cm, multiply by 100.
→ Example: 7.2 m = 7.2 × 100 = 720 cm

Centimetres (cm) to Metres (m):

→ 1 cm = 1/100 m = 0.01 m
→ To convert from cm to m, divide by 100.
→ Example: 1300 cm = 1300 / 100 = 13 m

Or

1300 cm = 1300 × 0.01 m 
= 1300 × 1/100m 
= 13 m

Centimetres (cm) to Millimetres (mm):

→ 1 cm = 10 mm
→ To convert from cm to mm, multiply by 10.
→ Example: 4.7 cm = 4.7 × 10 = 47 mm

Millimetres (mm) to Centimetres (cm):

→ 1 mm = 1/10 cm = 0.1 cm
→ To convert from mm to cm, divide by 10.
→ Example: 2000 mm = 2000 / 10 = 200 cm

Or

2000 mm = 2000 × 0.1 m 

= 2000 ×1/10m 

= 200 cm

Feet (ft) to inches (in):

→ 1 foot (ft) =12 inches (in)

Note: Foot is a singular form and feet is a plural form of the word “foot”.

→ To convert from feet to inches, multiply by 12.
→ Example: 3.2 ft = 3.2 × 12 in = 38.4 in

Inches (in) to Feet (ft):

→ 1 inch (in) = 1/12 foot (ft)
→ To convert from inches to feet, divide by 12.
→ Example: 60 in = 60 / 12 = 5 ft

These conversion relationships provide a convenient way to convert between different units of length allowing for accurate measurements across various contexts.

Direction (Examples 1 and 2): Kareena cycled for 3.4 kilometres to pick up her friend. They both reached school after travelling 2.7 kilometres. She reached school at 10:00 AM. After school, she directly returned from the school to her home and cycled for 5.5 kilometres. She reached home after school at 5:30 PM.

Read the question properly and observe the diagram carefully. Answer the following questions.

Example 1: What is the total distance in metres covered by Kareena on her way to school?

a) 600 m
b) 5500 m
c) 6100 m
d) 11600 m

Answer: c) 6100 m

Explanation: Total distance in metres covered by Kareena on her way to school = (3.4 + 2.7) km
                                                                                                                     = 6.1 km
                                                                                                                      = 6.1 × 1000 m
                                                                                                                       = 6100 m

Example 2: What is the total distance in centimetres covered by Kareena on the whole day?

a) 6100 cm
b) 11600 cm
c) 610000 cm
d) 1160000 cm

Answer: d) 1160000 cm

Explanation: Total distance in metres covered by Kareena on the whole day
= (3.4 + 2.7 + 5.5) km
= 11.6 km
= 11.6 × 1000 m
= 11600 m
= 11600 × 100 cm
= 1160000 cm