Question

# Convert 1kWh to S.I. unit of energy.A. $3.6\times 10^6 J$B. $3.6\times 10^8 J$C. $1.8\times 10^6 J$D. $1.8\times 10^8 J$

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Hint: kWh read as kilowatt hour, is a unit of energy. It can be verified that kW is a power unit (as 1kW=1000W) and hour (not an S.I. unit) is a time unit and power x time is work (or energy).

We know the expression for power:
$P=\dfrac{W}{t}$
which is nothing but work upon time. We are also aware of the fact that work done by a body is stored in the form of energy. Therefore, if we make a slight shift in the formula, we get:
$P \times t=W$
We get the work done which is stored in the form of energy.

Now, kW is 1000 Watts of power and 1 hour accounts for 3600 seconds. We know that, in S. I. units, hours will not work, so we choose seconds. Now, we multiply the terms we obtained, i.e.,
$1kWh = 1000W \times 3600s$
1kWh = 3600000 Ws
Shifting to scientific notations, we may write:
$1kWh = 3.6 \times 10^6 Ws$
Now, Ws is in S.I. but proper replacement for it would be Joules as we already derived above that power x time units gives energy units. So, we write simply,
$1kWh = 3.6 \times 10^6 J$

Therefore, we obtained the correct answer for the given question as option (A) $3.6 \times 10^6 J$ .

Additional Information: Joules is the unit of power as well as energy. We usually talk in terms of how much storage of energy we get upon doing work. Energy is something that has high physical significance but no direct mathematical relation.

Note: Recheck the scientific notation always once as the decimal placement creates some confusion sometimes specifically when negative powers of 10 are involved.