The density of nickel is 8908 kilograms per cubic metre. What is this value in grams per cubic centimetre?
Okay, so in this question, we’ve been told that the density of nickel, which we’ll call 𝜌 subscript 𝑛, is equal to 8908 kilograms per cubic metre. And we’ve been asked to convert this into grams per cubic centimetre. To do this, we need to recall a conversion between kilograms and grams and a conversion between cubic metres and cubic centimetres.
So, first of all, the conversion between kilograms and grams. We can recall that one kilogram is equivalent to 1000 grams. This is what the prefix “kilo” means. It means 1000. And so, what we can do is to replace this kilograms in our units for the density of nickel with 1000 grams. However, we’ll do that in a second.
Let’s first look at the conversion between metres cubed and centimetres cubed. To do this, we need to look at the conversion between metres and centimetres. We can recall that one metre is equivalent to 100 centimetres. Because the prefix “centi” means 100th of. Therefore, 100th of 100 is equal to one metre. And that’s why one metre’s equivalent to 100 centimetres.
Now because of this, we might think that one metre cubed is equivalent to 100 centimetres cubed. However, this is not the case. We need to be very careful here. Because if we have a cube, let’s say, of volume one metre cubed, then this is equivalent to the cube having side lengths one metre by one metre by one metre. And this is why the volume of the cube is one metre times one metre times one metre, which is one cubic metre. But then each one of these one-metre lengths are equivalent to 100 centimetres. And hence, one cubic metre is equivalent to 100 centimetres times 100 centimetres times 100 centimetres.
In other words, one cubic metre, that’s one metre cubed, is equivalent to 100 centimetres whole cubed. And so, on the left-hand side, we get one cubed and metres cubed. But one cubed is just one, so we get one metre cubed. And on the right-hand side, we get 100 cubed multiplied by centimetres cubed. Well, 100 cubed is equivalent to 1000000 and centimetres cubed is equal to centimetres cubed. Therefore, one cubic metre is actually equivalent of 1000000 cubic centimetres, not 100 cubic centimetres.
And now that we’ve taking care to understand this, we can start substituting things into our equation for the density of nickel. We see that the density of nickel 𝜌 subscript 𝑛 is equivalent to 8908. And then we’ll replace kilograms with 1000 grams, just as we saw here. And we’ll replace cubic metres with 1000000 cubic centimetres, just as we saw here. Then all that’s left to do is to evaluate 8908 multiplied by 1000 divided by 1000000. And the unit on the right-hand side of our equation now is going to be grams per cubic centimetres, just as we were asked to find in the question.
So, evaluating all the numbers, we find that the density of nickel ends up being 8.908 grams per cubic centimetres. This is equivalent to 8908 kilograms per cubic metre, but it is just written in different units. Therefore, our final answer is that the density of nickel is 8.908 grams per cubic centimetre.