## 1. Write the number as a percentage.

#### Note: ^{100}/_{100} = 1

#### 14.1666666667 =

#### 14.1666666667 × ^{100}/_{100} =

^{(14.1666666667 × 100)}/_{100} =

#### ^{1,416.66666667}/_{100} =

#### 1,416.66666667% ≈

#### 1,416.67%

#### (rounded off to a maximum of 2 decimal places)

#### In other words:

#### Multiply the number by 100...

#### ... And then add the percent sign, %

#### 14.1666666667 ≈ 1,416.67%

## 2. Write the number as an improper fraction.

#### 14.1666666667 can be written as an improper fraction.

#### (The numerator is larger than or equal to the denominator).

### Write down the number divided by 1, as a fraction:

#### 14.1666666667 = ^{14.1666666667}/_{1}

### Turn the top number into a whole number.

#### Multiply both the top and the bottom by the same number.

#### This number is: 10,000,000,000.

#### (1 followed by as many 0s as the number of digits after the decimal point)

^{14.1666666667}/_{1} =

^{(14.1666666667 × 10,000,000,000)}/_{(1 × 10,000,000,000)} =

^{141,666,666,667}/_{10,000,000,000}

## 3. Reduce (simplify) the fraction above: ^{141,666,666,667}/_{10,000,000,000}

(to the lowest terms, to its simplest equivalent form, irreducible).

#### To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.

### Factor both the numerator and the denominator (prime factorization).

#### In exponential notation (a^{n}):

#### 141,666,666,667 is a prime number, it cannot be factored into other prime factors

#### 10,000,000,000 = 2^{10} × 5^{10}

### Calculate the greatest (highest) common factor (divisor), GCF.

#### Multiply all the common prime factors by the lowest exponents.

#### But, the numerator and the denominator have no common factors.

#### GCF (141,666,666,667; 2^{10} × 5^{10}) = 1

### The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1).

So, the fraction cannot be reduced (simplified): irreducible fraction.

## 4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

#### A mixed number = an integer number and a proper fraction, of the same sign.

#### Example 1: 2 ^{1}/_{5}; Example 2: - 1 ^{3}/_{7}.

#### A proper fraction = the numerator is smaller than the denominator.

#### 141,666,666,667 ÷ 10,000,000,000 = 14, remainder = 1,666,666,667 =>

#### 141,666,666,667 = 14 × 10,000,000,000 + 1,666,666,667 =>

#### ^{141,666,666,667}/_{10,000,000,000} =

#### ^{(14 × 10,000,000,000 + 1,666,666,667)} / _{10,000,000,000} =

^{(14 × 10,000,000,000)} / _{10,000,000,000} + ^{1,666,666,667}/_{10,000,000,000} =

#### 14 + ^{1,666,666,667}/_{10,000,000,000} =

#### 14 ^{1,666,666,667}/_{10,000,000,000}

^{141,666,666,667}/_{10,000,000,000}: Equivalent fractions.

#### The above fraction cannot be reduced.

#### That is, it has the smallest numerator and denominator possible.

#### By expanding it we can build up equivalent fractions.

#### (Multiply the numerator & the denominator by the same number).

### Example 1. By expanding the fraction by 2:

^{141,666,666,667}/_{10,000,000,000} = ^{(141,666,666,667 × 2)}/_{(10,000,000,000 × 2)} = ^{283,333,333,334}/_{20,000,000,000}

### Example 2. By expanding the fraction by 4:

^{141,666,666,667}/_{10,000,000,000} = ^{(141,666,666,667 × 4)}/_{(10,000,000,000 × 4)} = ^{566,666,666,668}/_{40,000,000,000}

#### Of course, the above fractions are reducing...

#### ... to the initial fraction: ^{141,666,666,667}/_{10,000,000,000}