Question

Find the sum of 7 km 5 m, 8 m 6 cm and 4 m 9 mm.

Answer 1

Hint: The units given above are the units of distance. First of all convert the units given in the question in one unit like km, m, cm or mm. We are converting all the units in m. Some conversions into m. We know that $1km=1000m$, $1m=100cm$ and $1cm=10mm$. Using these conversions, convert all the units into m. We are showing the conversion of the first one i.e. 7 km 5 m using $1km=1000m$ we can convert 7 km into 7000 m and then add 7000 m into 5 m. Similarly you can do for the other two. And then add all the three distances.

Complete step-by-step answer:
We have to find the sum of the following:
7 km 5 m, 8 m 6 cm and 4 m 9 mm
All the units are for measuring the distance. First of all we are going to convert all the units in a single unit for addition.
We are going to convert the units into m.
In the below, we are representing the conversions:
$\begin{align}
  & 1km=1000m \\
 & 1m=100cm \\
 & 1cm=10mm \\
\end{align}$
Converting 7 km 5 m into m we get,
$1km=1000m$
Multiplying 7 on both the sides we get,
$7km=7000m$
Now, adding 7000 m into 5 m we get,
$\begin{align}
  & \left( 7000+5 \right)m \\
 & =7005m \\
\end{align}$
Converting 8 m 6 cm into m we get,
$1m=100cm$
Dividing 100 on both the sides we get,
$\dfrac{1}{100}m=1cm$
Converting 6 cm into m by multiplying 6 on both the sides we get,
$\begin{align}
  & \dfrac{6}{100}m=6cm \\
 & \Rightarrow 6cm=0.06m \\
\end{align}$
Adding 0.06 m into 8 m we get,
$\begin{align}
  & \left( 8+0.06 \right)m \\
 & =8.06m \\
\end{align}$
Converting 4 m 9 mm into m we get,
$1cm=10mm$
Dividing 10 on both the sides we get,
$\dfrac{1}{10}cm=1mm$
Multiplying 9 on both the sides we get,
$\dfrac{9}{10}cm=9mm$
Now, converting $\dfrac{9}{10}cm$ into m we get,
$\dfrac{1}{100}m=1cm$
Multiplying $\dfrac{9}{10}$ on both the sides we get,
$\dfrac{1}{100}\left( \dfrac{9}{10} \right)m=\dfrac{9}{10}cm$
$\begin{align}
  & \Rightarrow \dfrac{9}{1000}m=\dfrac{9}{10}cm \\
 & \Rightarrow 0.009m=\dfrac{9}{10}cm \\
\end{align}$
Converting 0.009 m to 4 m we get,
$\begin{align}
  & 4+0.009 \\
 & =4.009m \\
\end{align}$
From the above, we have converted:
7 km 5 m into 7005 m
8 m 6 cm into 8.06 m
4 m 9 mm into 4.009 m
Now, adding the converted distances we get,
\[\begin{align}
  & 7005.000m \\
 & +008.060m \\
 & \dfrac{+004.009m}{7017.069m} \\
\end{align}\]
Hence, the addition of 7 km 5 m, 8 m 6 cm and 4 m 9 mm is equal to 7017.069 m.

Note:You might have thought why we convert the units into m why not to km, cm, mm. You can convert the given units into any of these units. But here we have converted into m as when you see the units of the numbers; every number has one of the units in m.
7 km 5 m, 8 m 6 cm and 4 m 9 mm
When we convert the units into m then we have to do less number of conversions because every number has one unit in m.