Definition of Percent

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Percent is some part of something, expressed in numbers. Percent is denoted by the symbol %. Percent is used to show a part of something in the general quantity. To find the percent of something means to find the part of something in general amount. Some kinds of percent are commonly used in the banking sphere.

One percent is equal to one hundredth or 10-2. The general amount is 100%.
\[\frac{1}{100}=1\% ;  100\%=\frac{100}{100}=1 ;  50\%=\frac{50}{100}=\frac{1}{2} ;  25\%=\frac{25}{100}=\frac{1}{4} \]

Percentage may be more than 100%. If some value is 200% of a general amount, it means that this value is twice as big as a general amount. For example, two litres of water are equal to 200% of one litre of water.

Another example: If 100% of the number a is equal to a, 50% of the number a is equal to (\frac{1}{2}a\), 25% of the number a is equal to (\frac{1}{4}a\).
In order to convert a percent into a decimal number, we should divide the percent into 100.
For example:
25% = 25 ÷ 100 = 0,25;  56% = 56 ÷ 100 = 0,56; 340% =340 ÷ 100 = 3,4.

To convert decimal numbers into percent, we should divide this percent into 100.
For example:
0,24 ∙ 100 = 24%;  0,5 ∙ 100 = 50%;  1,23 ∙ 100 = 123%.

Finding Percentage Ratios
To find percent p% of the number a, we should multiply a by p and divide this number into 100:

\(\frac{a\cdot p}{100}\)

For example:
An employee’s wages is $3,000. This employee receives a 30% premium of the wages. How much money did the employee get?
x is the numerical value of the percent;
p= 30%;
100%=$3,000;
We can make the proportion:
$3,000 – 100%
x-30%
Or we can use the formula:
x=\(\frac{3000\cdot 30}{100}\)
x=900
To find percent of the number, we can represent percent as a decimal number:  x=0.3∙3000=900
Answer: employee received $900.

Finding 100% of the number
In order to find the number when we know the numerical value of the percent,  p%=b, we should multiply the numerical value of percent b by 100 and divide into percent p:

\(\frac{b\cdot 100}{p}\)

For example: Mary ate 6 candies. It was 20% of all the candies. How many candies did she have to begin with?
Let x equal all the candies;
p=20%;
20%=6;
We can make the proportion:
100% -x
20%-6
Or we can use the formula:
x=\(\frac{6\cdot 100}{20}\)
x=30
Alternative solution: x=6÷0.2=30
Answer: Mary had 30 candies.

Finding the percent ratio
In order to find the percentage ratio of number a to the number b, we should divide a into b and multiply it by 100:

\(\frac{a}{b}\cdot100\%\)

For example: 2 litres of juice contain 0.4 litres of apple juice. What is the percentage ratio of apple juice to «whole» juice?
Let x be a percent of apple in the juice;
100% – 2 litres;
x%= 0,4 litres of apple juice.
We can make the proportion:
100%-2
x%-0.4
Or we can use the formula:
x=\(\frac{0.4}{2}\cdot100\%\)
x=20%
Answer: 2 litres of juice contains 20% apple juice.

Percentage increasing
It is the “simple increasing”. If we have some period n, origin value \(a_0\) and the percent of this value p, which we get for year (or month), we can find our profit \(a_n\) by the  formula:

\(a_n\)\(=a_0\)\((1+\frac{n\cdot p}{100})\)

For example: A man has deposited $500 with a 10% yearly interest rate. How much money will he get after 3 years?
Original value = $500
Percent = 10%
Period (n) = 3 years
Find our profit by formula:
500(1+3∙10)=650
Answer: The man will get $650.

Compound Interest
Compound interest is commonly used in the banking area. If we have deposit a0 and percent p for the period of n years. To find our profit an we can use the formula of compound interest:

\(a_n\)\(=a_1\)\((1+\frac{p}{100})^{n}\)

For example: A depositor has deposited $1,000 for 2 years at 20% interest. How much money will the depositor have after 2 years?
\(a_0\)= $1,000;
Period (n) = 2 years;
p= 20%;
Find our profit by formula of compound interest:
\(a_n\)\(=2000\)\((1+\frac{20}{100})^{2}\)
\(a_n\)=2880
Answer: The depositor will have $2,880.