Percentages

Percent = amount present in 100 units of a solution.
Solution = Solute + Solvent
Solvent = liquid dissolving a solute
Solute = Material being dissolved in the solution

A drug is said to have a concentration of 100% when there is one gram in 1 cc (ml) of a solution (saline, D5, etc.).

What is a percentage?

A percentage is the top part of a fraction whose bottom part is 100.
So 50% means ‘half of’ and 25% means ‘a quarter of’. 100% means the complete quantity.

Why bother with them?

Percentages are useful because they make it very easy to compare things.

For example, suppose the marks in two successive tests are 67/80 and 51/60. It is not very easy to say which of these was best. Percentages use our ordinary number system of 10’s, 100’s etc and, because they are out of 100 rather than 10, we avoid a lot of the decimal points which make some people twitchy.

Changing a fraction to a %

Taking the example of the test mark of 67 out of 80,

Multiplying both sides of this equation by 100 gives us

RULE:- to change a fraction to a %, multiply it by 100.

Question:- What is the second test mark of 51/60 as a %? Try this yourself before looking.

Answer

so the mark in the second test was higher.

Changing a % to a fraction

RULE:- You simply turn it into a fraction by writing it over 100. Then cancel down if possible.

Example:- What is 35% as a fraction?

cancelling down to the simplest form by dividing the top and bottom by 5.

*** Remember that the value of a fraction remains unchanged when you multiply or divide both the top and the bottom by the same number. ***

Changing a decimal to a %

Suppose we want to write 0.27 as a %. Since a decimal is a kind of fraction, all we have to do is to multiply by 100. You just need to remember that each time you multiply by 10 the number becomes larger by a factor of 10 so the decimal point moves one place to the right. Multiplying by 100 moves it 2 places to the right. This neat rule is because decimals are fractions in our base ten number system.

So we find that 0.27 is the same as (0.27 x 100)% = 27%.

Similarly, 0.735 is the same as (0.735 x 100)% = 73.5%

and 7.46 is the same as (7.46 x 100)% = 746%.

RULE:- To change a decimal to a % we multiply by 100 which just moves the decimal point 2 places to the right.

Changing a % to a decimal     

RULE:- All we have to do is to divide by 100, so move the decimal point 2 places to the left.

Here are 3 examples to show you how to deal with all possible snags.

Example (1) What is 37% as a decimal?
Answer:- 37% is the same as 0.37.

Example (2) What is 25.5% as a decimal?
Answer:- 25.5% is the same as 0.255. (Notice that the percentage had a decimal point in here too.)

Example (3) What is 50% as a decimal? Answer:- 50% is the same as 0.50 = 0.5.
(The last zero just tells us that there is nothing in the 2nd position after the decimal point, so we can leave it out.)