Question

The distance between Hyderabad and Delhi is $ 1674.9\,{\rm{km}} $ by rail .How would you express this in centimetres? Also express this in scientific Form.

Answer 1

Hint: As we know that there are $ 100000\,{\rm{cm}} $ in $ 1\,{\rm{km}} $ place the decimal after first digit and express the number in the power of $ 10 $ to express it in scientific notation . Scientific notation is helpful in representing a very large or a very small number in a readable form.

Complete step by step answer:
Given the distance between Hyderabad and Delhi is $ 1674.9\,{\rm{km}} $ by rail
To convert the distance into centimetres multiply the given distance with $ 100000 $
$
1\,{\rm{km}} = 100000\,{\rm{cm}}\\
{\rm{1647}}{\rm{.9}}\,{\rm{km}} = 1647.9\,{\rm{km}} \times \dfrac{{100000\,{\rm{cm}}}}{{1\,{\rm{km}}}}\\
 = 164790000\,{\rm{cm}}
$
Now we have to convert the distance between Hyderabad and Delhi which is $ 16470000\,{\rm{cm}} $ to scientific notation. To convert the distance into scientific notation we have to put decimal after the first digit and then express the number in multiple of $ 10 $ .
Therefore
 $ 16470000\,{\rm{cm}} = 1.647 \times {10^7}\,{\rm{cm}} $ .
Hence the scientific notation for $ 16470000\,{\rm{cm}} $ is $ 1.647 \times {10^7}\,{\rm{cm}} $ .

Note:
while converting the Distance from kilometre to centimetre we must take into concern that we have to multiply the given distance by $ 100000 $ in order to determine the distance into centimetres it might be possible that some of us can divide the given distance which will lead to a Wrong answer.
While writing the scientific notation we must focus on the power of $ 10 $ it can be possible that one can count the wrong number up to which the $ 10 $ must be powered to obtain the correct result.