Question

Divide 6 km 2 hm 4 dam 4 m 9 dm 6 cm by 8.

Answer 1

Hint: First, we will use the scales \[1{\text{ km}} = 1000{\text{ m}}\], \[1{\text{ hm}} = 100{\text{ m}}\], \[1{\text{ dam}} = 10{\text{ m}}\], \[1{\text{ dm}} = \dfrac{1}{{10}}{\text{ m}}\], \[1{\text{ cm}} = \dfrac{1}{{100}}{\text{ m}}\] to convert all the units into meters and then add them together. Then we will divide the obtained value by 8 to find the required value.

Complete step-by-step answer:

We are given that 6 km 2 hm 4 dam 4 m 9 dm 6 cm is divided by 8.

First we will convert all the units in meters.

Using the scale \[1{\text{ km}} = 1000{\text{ m}}\] for 6 km, we get

$\Rightarrow 6{\text{ km}} = 6 \times 1000{\text{ m}}$

$\Rightarrow 6{\text{ km}} = 6000{\text{ m ......(1)}}$

Using the scale \[1{\text{ hm}} = 100{\text{ m}}\] for 2 hm, we get

$\Rightarrow 2{\text{ hm}} = 2 \times 100{\text{ m}}$

$\Rightarrow 2{\text{ hm}} = 200{\text{ m ......(2)}}$

Using the scale \[1{\text{ dam}} = 10{\text{ m}}\] for 4 dam, we get

$\Rightarrow 4{\text{ dam}} = 4 \times 10{\text{ m}}$

$\Rightarrow 4{\text{ dam}} = 40{\text{ m ......(3)}}$

Using the scale \[1{\text{ dm}} = \dfrac{1}{{10}}{\text{ m}}\] for 9 dm, we get

$\Rightarrow 9{\text{ dm}} = 9 \times \dfrac{1}{{10}}{\text{ m}}$

$\Rightarrow 9{\text{ dm}} = 0.9{\text{ m .......(4)}}$

Using the scale \[1{\text{ cm}} = \dfrac{1}{{100}}{\text{ m}}\] for 6 cm, we get

$\Rightarrow 6{\text{ cm}} = 6 \times \dfrac{1}{{100}}{\text{ m}}$

$\Rightarrow 6{\text{ cm}} = 0.06{\text{ m ......(5)}}$

Adding the equation (1), (2), (3), (4), (5) and 4 m, we get

$\Rightarrow \left( {6000 + 200 + 40 + 4 + 0.9 + 0.06} \right){\text{ m}}$

$\Rightarrow 6244.96{\text{ m}}$

Dividing the above values by 8, we get

$\Rightarrow \dfrac{{6244.96}}{8}$

$\Rightarrow 780.62{\text{ m}}$

Note:  In solving these types of questions, you should be familiar with the conversion of all the units in meters. If it is not given in the question that in which unit we have to convert, then we will convert the given value in meters. Avoid calculation mistakes.