## Reduce: ^{418}/_{119,447,100}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{418}/_{119,447,100}

#### The number above the bar is the numerator: 418

#### The number below the bar is the denominator: 119,447,100

#### The fraction bar means that the two numbers are dividing themselves:

^{418}/_{119,447,100} = 418 ÷ 119,447,100

#### Divide the numerator by the denominator to get fraction's value:

Value = 418 ÷ 119,447,100

### Introduction. Percent

#### 'Percent (%)' means 'out of one hundred':

#### p% = p 'out of one hundred',

#### p% = ^{p}/_{100} = p ÷ 100

### Note:

#### The fraction ^{100}/_{100} = 100 ÷ 100 = 100% = 1

#### Multiply a number by the fraction ^{100}/_{100},

... and its value doesn't change.

## To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

#### To calculate the greatest common factor, we build the prime factorization of the two numbers.

### Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 418 = 2 × 11 × 19;

418 is not a prime, is a composite number;

#### 119,447,100 = 2^{2} × 3^{2} × 5^{2} × 17 × 37 × 211;

119,447,100 is not a prime, is a composite number;

** Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself. *

* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

### Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

#### Multiply all the common prime factors, by the lowest exponents (if any).

#### gcf, hcf, gcd (418; 119,447,100) = 2

### Divide both the numerator and the denominator by their greatest common factor.

^{418}/_{119,447,100} =

^{(2 × 11 × 19)}/_{(22 × 32 × 52 × 17 × 37 × 211)} =

^{((2 × 11 × 19) ÷ 2)} / _{((22 × 32 × 52 × 17 × 37 × 211) ÷ 2)} =

^{(11 × 19)}/_{(2 × 32 × 52 × 17 × 37 × 211)} =

^{209}/_{59,723,550}

## The fraction is now reduced to the lowest terms.

^{209}/_{59,723,550} is a proper fraction.

#### A proper fraction: numerator smaller than denominator.

## Rewrite the end result, continued below...

## Rewrite the end result:

### As a decimal number:

^{209}/_{59,723,550} =

#### 209 ÷ 59,723,550 ≈

#### 0.000003499457 ≈

#### 0

### As a percentage:

#### 0.000003499457 =

#### 0.000003499457 × ^{100}/_{100} =

#### ^{0.000349945708}/_{100} =

#### 0.000349945708% ≈

#### 0%

#### In other words:

#### 1) Calculate fraction's value.

#### 2) Multiply that number by 100.

#### 3) Add the percent sign % to it.

## Final answer

continued below...

## Final answer:

:: written in three ways ::

## As a proper fraction

(numerator smaller than denominator):

^{418}/_{119,447,100} = ^{209}/_{59,723,550}

## As a decimal number:

^{418}/_{119,447,100} ≈ 0.000003499457 ≈ 0

## As a percentage:

^{418}/_{119,447,100} ≈ 0%

## More operations of this kind:

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