We use different standard units to measure length and distance depending on the size of the object or the distance being measured. In this chapter, we explore various units of measurement and the relationships between them.
Identify whether to use Metre (m) or Centimetre (cm) for measuring the following:
Using a double number line, we can visualize the relationship between metres and centimetres:
Comparing lengths requires converting them to the same unit before applying comparison operators ($<$, $=$, $>$).
Heights of some of the world's tallest statues:
For measuring long distances, we use specialized tools and the unit Kilometre (km).
When we walk $1,000\text{ m}$, we say we have walked $1\text{ km}$.
$$\text{Kilo} = \text{Thousand}$$
$$1,000\text{ m} = 1\text{ km}$$
To measure very small objects, we divide a centimetre into ten equal parts called Millimetres (mm).
$$1\text{ cm} = 10\text{ mm}$$
Small marks on a standard ruler represent millimetres, allowing for high precision when measuring small items like sprouts, small screws, or fingernails.
Understanding conversions is essential for performing arithmetic operations on lengths.
When adding or subtracting lengths, group similar units together or convert all quantities to the same unit before calculating.
Example (Addition): $3\text{ km } 450\text{ m} + 4\text{ km } 650\text{ m}$
Example (Subtraction): $63\text{ m} - 16\text{ m } 75\text{ cm}$
Multiplication Example: If $1\text{ m } 80\text{ cm}$ of cloth is needed for one shirt, how much is needed for $20$ shirts?
$$20 \times 1\text{ m } 80\text{ cm} = (20 \times 1\text{ m}) + (20 \times 80\text{ cm})$$
$$= 20\text{ m} + 1600\text{ cm} = 20\text{ m} + 16\text{ m} = 36\text{ m}$$
Division Example: If a road of $12\text{ km } 600\text{ m}$ is laid equally over $6$ days, how much is laid each day?
$$(12\text{ km } 600\text{ m}) \div 6 = 2\text{ km } 100\text{ m}\text{ per day}$$
In daily life, we also use non-metric units like Inches and Feet to measure height and depth.