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### Find the Ratio: 0.0625 : 0.09375

```Date: 05/15/2003 at 15:31:38
From: Faisal
Subject: Ratio

find the ratio between 0.0625:0.09375 and please tell me how to do it.

Thank you, Dr. Maths,
Faisal
```

```
Date: 05/15/2003 at 17:22:25
From: Doctor Ian
Subject: Re: Ratio

Hi Faisal,

There are a few different ways you might approach this.  One is to
divide the larger number by the smaller one.  For example, if you
have a ratio of

12:138

doing the division

1 1.5
________
12 ) 1 3 8.0
1 1
---
1 8
1 2
---
6 0
6 0
---
0

shows us that this is the same as the ratio 1:11.5.  What do you get
when you try this with your numbers?

A second thing we can do is scale the values in the ratio by the same
amount until they don't look quite as intimidating. For example, a
ratio of 2:5 is the same as a ratio of 20:50 or a ratio of 200:500.
(Do you see why?)

So we can keep multiplying both terms by 10 until we get rid of the
decimal point:

0.0625  :    0.09375
0.625        0.9375
6.25         9.375
62.5         93.75
625          937.5
6250         9375            <-- Same ratio, different values

This looks easier to reduce, doesn't it?  We can look for common
factors, and eliminate them, e.g.,

6250 : 9375

= 1250 * 5 : 1875 * 5

= 1250 : 1875

Where before we scaled _up_ by a factor of 10, now we're scaling
_down_ by a factor of 5.  But it's the same idea.

Can you find other factors that these values have in common, and
eliminate them?

A third thing you can do is look for patterns that might work out
nicely.  In this case, I happen to know that 1/8 is 0.125, which means
that 5/8 is 0.625, so that means that 0.0625 is 1/10 of that, or 5/80.
So what if I multiply both items by 80?

0.0625 : 0.09375
*    80        80
------   -------
5       7.5

That's a lot easier to deal with, isn't it?  This third approach
requires you to be pretty comfortable with fraction/decimal
conversions, so don't feel that this is something that should have
jumped out at you. Mostly I was just trying to give you a sense of
some of the different ways that you can tackle ratio problems.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Ratio and Proportion

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