Question

I have no idea:

David drove a distance(d) of 187km, to 3 sig.fig. He used 28 litres of petrol(p), to 2 sig.fig.
The petrol consumption(c)in km per litre is given by the formula: c= d/p
By considering bounds, work out the value of c, to a suitable degree of accuracy. You must show your working and give a reason for your answer.
Thank You!

Answer 1

So we have the formula:
`c= (d)/(p)`
where

`d` is the distance in kilometers

`p` is the petrol in liters

`c` is the petrol consumption in kilometers per liter

We now for our problem that David drove a distance of 187 km, so
`d=187`. We also know that he used 28 liters of petrol, so
`p=28`. Lets replace those values in our formula to find the petrol consumption:

`c= (d)/(p)`

`c= (187)/(28)`

`c=6.67857`

Now, remember that are some rules to determine the number of significant figures in a number:
1. Non-zero digits are always significant figures.
2. A zero between tow significant figures is always a significant figure.

Applying those tow rules we realize that
`c` has 6 significant figures, whereas
`d` has three significant figures and
`p` only two. In mathematical operations with significant figures, the answer should be given with the same significant figures as the number with least significant figures involved in the operations. In our case, that number is
`p`, and
`p` has two significant figures, so our answer should have 2 significant figures. To give our answer with 2 significant figures, we are going to round it:

`c=6.67857`

`c=6.7`

We can conclude that the patrol consumption of David's vehicle is 6.7 kilometers per liter.