Question

Express as metres using decimals.
(a) 15 cm
(b) 6 cm
(c) 2m 45 cm
(d) 9 m 7 cm
(e) 419 cm

Answer 1

Hint: We had to only change the sign convention of the given lengths to metres and that can be done by using the conversion formula that is 100 cm = 1 m or we can say that 1 cm = \[\dfrac{1}{{100}}\].

Complete step-by-step answer:
As we know that 1 m = 100 cm.
So, dividing both sides of the above equation by 100. We get,
1 cm = \[\dfrac{1}{{100}}\] m (1)
So, now let us solve the different parts step by step.

(a) If 1 cm = \[\dfrac{1}{{100}}\] m
Then, 15 cm = \[15 \times \dfrac{1}{{100}}\] = \[\dfrac{{15}}{{100}}\] m = 0.15 metres

(b) 6 cm = \[6 \times \dfrac{1}{{100}}\] = \[\dfrac{6}{{100}}\] m = 0.06 metres

(c) Now in 2m 45cm we had to change 45cm to metres and then add that with 2metres.
So, 45 cm = \[45 \times \dfrac{1}{{100}}\] = \[\dfrac{{45}}{{100}}\] m = 0.45 metres
So, 2m 45cm = (2 + 0.45) metres = 2.45 metres

(d) Now in 9m 7cm we had to change 7cm to metres and then add that with 9 metres.
So, 7 cm = \[7 \times \dfrac{1}{{100}}\] = \[\dfrac{7}{{100}}\] m = 0.07 metres
So, 9m 7cm = (9 + 0.07) metres = 9.07 metres

(e) 419 cm = \[419 \times \dfrac{1}{{100}}\] = \[\dfrac{{419}}{{100}}\] m = 4.19 metres

Note:- Whenever we come up with this type of problem where we are asked to change the unit from centimetres to metres in decimals then we have to just divide the given number by 100 and change the unit from centimetres to metres because 1 m = 100 cm. This will be the easiest and efficient way to find the solution of the problem.