Question

How do you convert $ 7.5 \times {10^4}J $ into Kilojoules?

Answer 1

Hint: For expressing the physical quantities we use several units, the standard unit of a physical quantity represents its unit value. For example S.I. a unit of distance is 1 meter, one meter is a specified distance that is chosen to be taken as a standard for measuring the distance. But some areas involve large quantities of the physical quantities, so we have to use the bigger units of the physical quantities to express it conveniently. For example, the distance between any two cities is very large, so it is better to write it as 82 km then 820000 m. All the units of a physical quantity are related to each other and can be converted from one unit to another easily.

Complete step-by-step answer:
We know that $ 1\;kJ = 1000\;J $
1000 means 10 multiplied with itself 3 times, so –
 $
  1000 = 10 \times 10 \times 10 \\
   \Rightarrow 1000 = {10^3} \;
  $
So for converting $ 7.5 \times {10^4}J $ into Kilojoules we divide the expression in Joules by $ {10^3} $
 $
  \dfrac{{7.5 \times {{10}^4}}}{{{{10}^3}}} = 7.5 \times {10^{4 - 3}} \\
   \Rightarrow 7.5 \times {10^4}\;J = 7.5 \times 10 = 75\;kJ \;
  $
Hence, $ 7.5 \times {10^4}J $ in Kilojoules is $ 75\;kJ $ .
So, the correct answer is “ $ 75\;kJ $ ”.

Note: In scientific notation, we express too large or too small numbers in the decimal form for a convenient expression. A number written as a product of a number lying between 1 and 10 and a power of 10 is said to be written in the scientific notation. For example, $ N \times {10^m} $ is a scientific notation where N lies between 1 and 10 and contains only significant figures. We can solve the given equation by either converting $ {10^4} $ into 10000 or by converting 1000 into $ {10^3} $ . We can solve all the similar questions using a similar approach.