## Percentage

Percentage is a number or ratio that is expressed as a fraction of 100. It is often marked in with percentages sign “%” or “pct”. The word “percentages” means “out of 100” or “per 100”.  Also number can be expressed as a fraction of 1,000, that system uses terms “per mil” and “millage”.

Percentages are used to express how large or small one quantity is relative to another quantity. The first quantity usually represents a part of, or a change in the second quantity. For example: an increase of \$ 0.15 on a price of \$ 3.00 is an increase by a fraction of 0.15/3.00 = 0.05. Expressed as a percentage this increase is in amount of 6%.

Percentages are usually used to express values between zero and one, but they can be used to express any ratio as a percentage.

For example: 125% is 1.25 and -45% is -0.45.
The percentage value is computed by multiplying the numeric value of the ratio by 100.

For example: to find 40 apples as a percentage of 1250 apples. First of all we need to compute the ratio 40/1250 = 0.032 and then we need to multiply with 100 and the result is 3.2%.

It is also possible to calculate a percentage of a percentage. First of all we need to convert both percentages to fractions of 100, or to decimals and then we need to multiply them.

In our example we will calculate 50% of 60%:
(50/100) * (60/100) = 0.50 * 0.60 = 0.30 = 30/100 = 30%

Related units
Per mil (‰)    1 part in 1,000
Basic point     1 part in 10,000
Per cent mille (pcm) 1 part in 100,000
Parts-per notation
Concentration

History
A long before the existence of the decimal system computations were made in fractions which were multiplied with of 1/100. In ancient Rome Augustus levied a tax of 1/100 on goods sold at auction known as “ centesima rerum venalium”. Computations with these fractions were similar to computing of percentages. The word “percent” is derived from the Latin word “per centrum” that is meaning “by the hundred”.

The percentages are not used only in math. They are also used in daily life, in economics and other sciences. The percentages are also vital part of modern sport statistics.

## History of decimal fractions

Decimal fractions were first developed and used in the 1st century BC by the Chinese. After sometime they spread to the Middle East and from there to Europe.

The  Immanuel Bonfils ( Jewish mathematician) invented decimal fraction around 1350, but didn’t develop any notation to represent them. A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century.

→ Learn  how to add, subtract, divide or multiply fractions. Check your own fraction calculations or practice online with  fractions calculator

## Rational number

A rational number is any number that can be expressed as the quotient or fraction (a/b) of two integers, with the denominator not equal to zero. Any rational number with a denominator whose only prime factors are 2 or 5 may be precisely expressed as a decimal fraction.

Example:
1/2=0.5
1/20=0.05
1/5=0.2
1/4=0.25
1/25=0.04

But if the rational numbers denominator has any prime factors other than 2 or 5, decimal fraction cannot be expressed as finite decimal expansion, and has a unique eventually repeating infinite decimal expansion.

Example:

1/3=0.333333… (with 3 repeating)
1/9=0.111111… (with 1 repeating)

## Decimal to fraction calculator

Before you try decimal to fraction calculator, find out more about decimal fraction. A decimal fraction is a fraction whose denominator (the bottom number) is a power of ten such as 10, 100, 1000…

Decimal to fraction calculator is an online calculator and helps you to convert a decimal number into fraction.

Decimal fractions are expressed without a denominator, the decimal separator (point) being inserted into the numerator at the position from the right corresponding of ten of the denominator.

Example:
35/100 is a decimal fraction and it can be shown as 0.35
35/1000 is a decimal fraction and it can be shown as 0.035

Integral part of a decimal number is the part to the left of the decimal separator, and the part from the decimal separator to the right is the fractional part.

→ Learn very easy how to add, subtract, divide or multiply fractions. Check your own fraction calculations or practice online with this fractions calculator

## Decimal system

The decimal numeral system (called base ten ordinary) has ten as its base. This numerical base is most used by modern civilizations. Decimal notation is system of writing numbers in a base-10 numeral system. Through the history few system was developed. Examples are, Roman numerals, Brahmi numerals and Chinese numerals as well as the Hindu-Arabic numerals used by speakers of many European languages.

When people who use  Hindu-Arabic numerals speak of decimal notation, they often mean not just decimal numeration they also mean decimal fractions all conveyed as a part of a positional system. Positional decimal system uses symbols (digits) include zero for the ten values (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any number. These values are often used with a decimal separator (also called point) which indicates the start of fractional part.

## Mixed numbers or mixed fractions

A mixed numeral (often called a mixed fraction or a mixed number) is the sum of a non-zero integer and proper fraction. The whole and fractional parts of the number are written next to each other. A mixed number can be converted to an improper fraction in few steps. First of all the mixed number has to be written as a sum, then the whole number must be converted to an improper fraction with the same denominator as the fractional part. The resulting sum is improper fraction. The example will be shown below.

Similarly an improper fraction can be converted to a mixed number. First of all the numerator must be divided by the denominator. In our example , 9 divided by 4 and the result is 2 with remainder 1. The “2” becomes the whole number part of mixed number and the remainder becomes the numerator of the fractional part. The new denominator is the same as the denominator of improper fraction, in our example that is 4.

→ Learn very easy how to add, subtract, divide or multiply fractions. Check your own fraction calculations or practice online with this fractions calculator

## Comparing fractions

Comparing fractions is simply, if fractions have same denominator. In that case we only compare numerators of fractions. If two positive fractions have the same numerator, then the fraction with smaller denominator is larger number. To compare the fractions with different numerators and denominators, we need to find a common denominator.

For example: → Learn very easy how to add, subtract, divide or multiply fractions. Check your own fraction calculations or practice online with this fractions calculator

## How to multiply fractions

Multiplication of fractions is simple. How to multiply fractions ? You just need to multiply numerators and multiply denominators. A short cut of multiplying fractions is called “cancellation”. In effect, we reduce the answer to lowest terms during multiplication.

Example: How to multiply fractions How to multiply fractions online ? Now, check your own fraction calculations or practice online with this fractions calculator

## How to divide fractions

Division of fractions is similar as multiplication of fractions. How to divide fractions ?  You just need to turn second fraction (the one you want to divide by) upside down and just multiply as example below.

Example: How to divide fractions

How to divide fractions online ? Now, Check your own fraction calculations or practice online with this fractions calculator → Learn how to multiply fractions

## How to subtract fractions

Subtraction of fractions is in essence the same process as adding of fractions. How to subtract fractions : find a common denominator, and change each fraction to an equivalent fraction with the chosen common denominator.

Subtracting fractions with different denominators How to subtract fractions online ? Now, Check your own fraction calculations and  practice online with this fractions calculator