(a) 1 m = ________ cm.
(b) 1 sq cm = ________ cm × 1 cm.
(c) 1 sq m = 1 m × ________ m = 100 cm × ________ cm.
(d) 1 sq m = ________ sq cm.
(a) 1 m = 100 cm.
(b) 1 sq cm = 1 cm × 1 cm.
(c) 1 sq m = 1 m × 1 m = 100 cm × 100 cm.
(d) 1 sq m = 10000 sq cm.
Idea: A square unit means length × length using the same unit.
(a) Convert metre to centimetre
We know: (1 ext{m} = 100 ext{cm}).
(b) What is 1 square centimetre?
(1 ext{sq cm}) means a square of side (1 ext{cm}).
So: (1 ext{sq cm} = 1 ext{cm} imes 1 ext{cm}).
(c) Write 1 square metre in two ways
First, in metres: (1 ext{sq m} = 1 ext{m} imes 1 ext{m}).
Now change each metre to centimetres:
(1 ext{m} = 100 ext{cm})
So: (1 ext{sq m} = 100 ext{cm} imes 100 ext{cm}).
(d) How many square centimetres in 1 square metre?
Multiply the numbers: (100 imes 100 = 10{,}000).
Therefore: (1 ext{sq m} = 10{,}000 ext{sq cm}).
Summary:
(1 ext{m} = 100 ext{cm})
(1 ext{sq cm} = 1 ext{cm} imes 1 ext{cm})
(1 ext{sq m} = 1 ext{m} imes 1 ext{m} = 100 ext{cm} imes 100 ext{cm} = 10{,}000 ext{sq cm})