Question

The height of a person is $1.75m$. Express it into cm and mm.

Answer 1

Hint: First we will separate the decimal part of the given height of the person from the integer part. Now we will write the decimal part in a fraction. Now we will use the relation between the units $1m=100cm$ and $1m=1000mm$. From this relation we will convert the integer part as well as the decimal part into required units.

Complete step-by-step answer:
Given that, height of a person is $1.75m$.
We can write $1.75$ as $1+0.75$, here $1$ is the integer part and $0.75$ is the decimal part.
So $1.75m=1m+0.75m$.
To convert $1.75m$ into centimeters and millimeters we need to first convert the integer part and decimal part into centimeters and millimeters.
We know that $1m=100cm$ and $1m=1000mm$ so the conversion of integer part is completed as of now.
Now we are converting the integer part into centimeters and millimeters as
Let $0.75m=x\text{ cm}$
$\begin{align}
  & \Rightarrow 0.75m=x\text{ cm} \\
 & \Rightarrow 0.75\times 1m=x\text{ cm} \\
\end{align}$
Substituting $1m=100cm$ in above equation, then we will get
$\begin{align}
  & 0.75\times 1m=x\text{ cm} \\
 & \Rightarrow 0.75\times 100\text{ cm}=x\text{ cm} \\
 & \Rightarrow 75\text{ cm}=x\text{ cm} \\
 & \Rightarrow 0.75m=75\text{ cm} \\
\end{align}$
Now the height of the person in centimeters is written as
$\begin{align}
  & 1.75m=1m+0.75m \\
 & \Rightarrow 1.75m=100cm+75cm \\
 & \Rightarrow 1.75m=175cm \\
\end{align}$
$\therefore $ Height of the person in centimeters is $175cm$.
Now we have the integer part of given height in millimeters, so we need to convert the decimal part into millimeters.
Let $0.75m=y\text{ mm}$
$\begin{align}
  & \Rightarrow 0.75m=y\text{ mm} \\
 & \Rightarrow 0.75\times 1m=y\text{ mm} \\
\end{align}$
Substituting $1m=1000mm$ in above equation, then we will get
$\begin{align}
  & 0.75\times 1m=y\text{ mm} \\
 & \Rightarrow 0.75\times 1000\text{ mm}=y\text{ mm} \\
 & \Rightarrow 750\text{ mm}=y\text{ mm} \\
 & \Rightarrow 0.75m=750\text{ mm} \\
\end{align}$
Now the height of the person in millimeters is written as
$\begin{align}
  & 1.75m=1m+0.75m \\
 & \Rightarrow 1.75m=1000mm+750mm \\
 & \Rightarrow 1.75m=1750mm \\
\end{align}$
$\therefore $ Height of the person in millimeters is $1750mm$.

Note: We can directly find the height of the person in centimeter and millimeter by using$1m=100cm$ and $1m=1000mm$ as
$\begin{align}
  & 1.75m=1.75\times 1m \\
 & \Rightarrow 1.75m=1.75\times 100cm \\
 & \Rightarrow 1.75m=175cm \\
\end{align}$ and $\begin{align}
  & 1.75m=1.75\times 1m \\
 & \Rightarrow 1.75m=1.75\times 1000mm \\
 & \Rightarrow 1.75m=1750mm \\
\end{align}$
From both the methods we got the same answer.