# Simple units conversion question

Homework Statement:
Show that the cost of this wasted energy will be about £4, if electrical energy is
charged at 20 p per kWh. given that total energy wasted energy is 7.5(6) × 107 (J)
Relevant Equations:
no equations
as it wants the units kWh does that not mean you times by 3600 to go from s --> h and to go from W to kilowatt --> you divide the value by 1000

yet they divided by 3600 to get answer

phyzguy
Unit conversions can be confusing, and it's easy to mix up whether you should multiply or divide by the conversion factor. The best way is to carry along the units in your calculation, canceling them along the way , like this:
$$1\, kWh = 1000 \, W h = 1000 \frac{J}{s}h \times 3600 \frac{s}{h} = 3.6 \times 10^6 J$$
so:
$$7.5 \times 10^7 J = \frac{7.5 \times 10^7 J}{3.6 \times 10^6 \frac{J}{kWh} }= 20.8\, kWh$$

PeroK and berkeman
berkeman
Mentor
yet they divided by 3600 to get answer
As shown by @phyzguy it is best to carry units along in your calculations. Units on the LHS and RHS of each equation should match. A helpful trick for doing units conversions is to "multiply by one", where the "one" has the units you want to end up with in the numerator, and the units you want to cancel out in the denominator.

Like this: Convert 60 km/hr into m/s:

$$1 = 3600 \frac{s}{hr} = 60 \frac{s}{min} * 60 \frac{min}{hr}$$

$$60 \frac{km}{hr} * \frac{1 hr}{3600 sec} * \frac{1000 m}{1 km} = 16.7 m/s$$

Last edited:
phyzguy
vela
Staff Emeritus
Homework Helper
It also helps to have an idea of whether you should get a bigger or smaller number after the conversion. For example, 1 km and 1000 m both describe the same length, but because it takes a bunch of meters to make a kilometer, i.e., a kilometer is longer than a meter, you need more meters (1000) than kilometers (1) to specify the same length.

In your case, you want to convert from Joules to kWh. A joule is a watt-second, which is smaller than a watt-hour, so for a given amount of energy, there would be more watt-seconds than watt-hours. Therefore, going from joules to watt-hours, you should expect to get a smaller number. Given the choice of multiplying by 3600 or dividing by 3600, which calculation is going to yield a smaller number? Dividing. So you should divide by 3600, not multiply.

berkeman
Mark44
Mentor
@bonbon22, please don't add "A level" to your thread titles, even if it might be technically accurate, because it can be confusing to readers here. At this forum, titles can be tagged as B-, I-, and A-level, indicating that the question is at one of these levels: Basic (high school), Intermediate (undergraduate), or Advanced (graduate).

berkeman
Mentor