## Category Archives: Uncategorized

## 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

Grade (slope)

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 calculato**r 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**