Ratio questions

Question

Earth has an approximate radius of 6000 km

Write down the ratio of the radius of the Earth to each radii of these planets, giving your answer in the form 1:n a.

Saturn = 58 000 km b.

Uranus = 25 000 km c.

Mars = 3 300 km

Answer 1

Hi Leo,

Ratios are used when we want to compare two things (in this case, the planets).

The first thing we always have to check when writing ratios, is do these two things have the same units?

In this case, the Earth and each planet's radii are expressed in kilometers (km), so we're all set with units!

(a) Saturn (r=58,000km)

Let's do this one together.

The problem asks us for the ratio of Earth's radius to Saturn's radius. Let's write it in words first.

6000 km to 58,000 km.

It turns out, in mathematics, we use the symbol " : " as a way of expressing "to". The colon symbol tells us we're comparing two things.

6,000 : 58,000

But, we're not done! We're asked to write the answer in the form "1 to n" or "1 : something".

How do we do that?

In our expression above, we want a 1 on the lefthand side.

How do we get a 1 on the lefthand side? This is called simplifying.

Well, if we divide 6,000/6,000 = 1.

But, what we do to the lefthand side, we have to do to the right. So, divide both numbers by 6000.

58,000/6,000 = 9.66

So, our final answer for (a) is 1 : 9.66 !

Now, why don't you try doing (b) and (c) on your own (:

Hope this helps!