Note before; I have searched the site and can't find an answer to this question, so that I wouldn't make a duplicate. I couldn't find the answer already so I either didn't search properly, or this questions is embarrassingly easy! I will not be proud of either outcome.
How can I convert a decimal ratio to a percentage?
For example, I am reading some data collection results, for measurements taken over a period of time. Lets imagine we measured what proportion of meat sold in a supermarket was either A (sausages), or B (burgers) assuming they sell no other meat! The following is stated in the results:
The ratio of A to B in 2009 was 0.11. Now in 2012, it is 0.20. We predict that by 2020 A will be between 2.5 and 3.0.
I have translated that to the following statement in my head (question marks indicate conversations I am sceptical of):
In 2009 11% of meat sold was sausages (so 89% was burgers?). Now in 2012, it is %20 meat sold? We predict that by 2020 for every burger sold, between 2.5 and 3 sausages will have been sold? That means upto %75 percent of sales will become sausages, burgers will form ony 25%?
Is it that simple, have I correctly transferred the ratios into percentages? What is the generally accepted method of converting these decimal ratio figures into a percentage?
I know this probably seems like childish arithmetic, but I haven't done this in many years!
Best Answer
Your first two interpretations aren't correct. Your third interpretation is.
Once you interpret the first two quantities in the way that the third was, you should see where your mistake lies.
But, for completeness:
The phrase "The ratio of $A$ to $B$" refers to the quotient $A/B$.
I think it's better not to use decimals here, but rather say, for example, "the ratio of $A$ to $B$ is $1:9$ (one to nine)". This would mean that for every $9$ units of $B$ sold, one unit of $A$ was sold (this is the manner in which the information for 2020 is phrased).
If you wanted the percentage of the total amount ($A+B$) that $A$ is, it would be expressed as a decimal as $A\over A+B$. If the ratio $A$ to $B$ is given as a decimal $x$, then the percentage of the total that $A$ is would be expressed as a decimal using the formula ${x\over x+1}$.
For example, in 2009, the ratio of sausages to burgers was $x=.11\approx1/9$. The percentage of sausages sold in 2009 was $ {1/9\over 1+1/9} ={1\over9+1}={1\over 10}$. So the percentage is $ 10\%$.
This should make sense, as you can do the computation somewhat differently:
In 2009, for every $9$ burgers sold, $1$ sausage was sold (here, you just make up numbers that give the correct ratio). So the percentage of sausage sold in 2009 was ${1\over 1+9}\cdot 100\% =10\%$ (part to the whole).