Question

How do you express $105cm$ in metres?

Answer 1

Hint: The given question has length which is measured in centimeters and we have to express it in metres. We know that to convert centimeters to meters we have to multiply the given length by \[\dfrac{1}{100}\] to get the length in meters. That is, \[1cm=\dfrac{1}{100}m\]. Hence, we will get $105cm$ in metres.

Complete step-by-step solution:
According to the given question, we are given a question which has length expressed in centimetres, and we have to express it in meters.
We know that the SI unit for length is meters. SI unit refers to the International System of Units.
Let’s look in a bit deeper for the various units in which length can be expressed.
We have,
\[km\to hm\to dam\to m\to dem\to cm\to mm\]
For example – if we have to convert 1 kilometre to meters, then we will multiply by that many numbers of 10. That is
\[1km=10\times 10\times 10m\]
\[\Rightarrow 1km=1000m\]
And if we have to convert 1 meter to kilometre, then we will divide by that many numbers of 10. That is,
\[1m=\dfrac{1}{10\times 10\times 10}km\]
\[\Rightarrow 1 m=\dfrac{1}{1000}km\]
So, we are given $105cm$ which we have to express in metres. So from the above chart, we can see that to convert centimetres to metres, we will have to divide by \[100\] or multiply by \[\dfrac{1}{100}\].
And we get,
\[105cm\times \dfrac{1m}{100cm}\]
Solving further we have,
\[\Rightarrow \dfrac{105}{100}m\]
\[\Rightarrow 1.05m\]
Therefore, we get that \[105cm=1.05m\].

Note: The conversion from one unit to another is based on the below mentioned chart, that is,
\[km\to hm\to dam\to m\to dem\to cm\to mm\]
While converting/moving from a larger unit (like kilometre) to a smaller unit (like metre), we multiply by that many multiples of 10. And when converting from a smaller unit to a larger unit, we divide by that many multiples of 10.
\[\to multiply\text{ }by\text{ }multiples\text{ }of\text{ }10\]
\[km\to hm\to dam\to m\to dem\to cm\to mm\]
\[\leftarrow divide\text{ }by\text{ }multiples\text{ }of\text{ }10\]