# Convert the decimal number 24.57879. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

## Convert 24.57879

## 1. Write the number as a percentage.

#### Multiply the number by ^{100}/_{100}

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

#### The value of the number does not change when multiplying by ^{100}/_{100}

#### 24.57879 =

#### 24.57879 × ^{100}/_{100} =

^{(24.57879 × 100)}/_{100} =

#### ^{2,457.879}/_{100} =

#### 2,457.879% ≈

#### 2,457.88%

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

#### In other words:

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

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

#### 24.57879 ≈ 2,457.88%

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

#### 24.57879 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:

#### 24.57879 = ^{24.57879}/_{1}

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

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

#### This number is: 100,000.

#### 1 followed by as many 0-s as the number of digits after the decimal point.

^{24.57879}/_{1} =

^{(24.57879 × 100,000)}/_{(1 × 100,000)} =

^{2,457,879}/_{100,000}

## 3. Reduce (simplify) the fraction above: ^{2,457,879}/_{100,000}

(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}):

#### 2,457,879 = 3 × 83 × 9,871

#### 100,000 = 2^{5} × 5^{5}

### 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 (3 × 83 × 9,871; 2^{5} × 5^{5}) = 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.

#### 2,457,879 ÷ 100,000 = 24, remainder = 57,879 ⇒

#### 2,457,879 = 24 × 100,000 + 57,879 ⇒

#### ^{2,457,879}/_{100,000} =

#### ^{(24 × 100,000 + 57,879)} / _{100,000} =

^{(24 × 100,000)} / _{100,000} + ^{57,879}/_{100,000} =

#### 24 + ^{57,879}/_{100,000} =

#### 24 ^{57,879}/_{100,000}

^{2,457,879}/_{100,000}: Equivalent fractions.

#### The above fraction cannot be reduced.

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

#### 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 4:

^{2,457,879}/_{100,000} = ^{(2,457,879 × 4)}/_{(100,000 × 4)} = ^{9,831,516}/_{400,000}

### Example 2. By expanding the fraction by 7:

^{2,457,879}/_{100,000} = ^{(2,457,879 × 7)}/_{(100,000 × 7)} = ^{17,205,153}/_{700,000}

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

#### ... to the initial fraction: ^{2,457,879}/_{100,000}

## :: Final answer ::

Written in 4 different ways

## As a reduced (simplified) positive improper fraction:

24.57879 = ^{2,457,879}/_{100,000}

## As a mixed number:

24.57879 = 24 ^{57,879}/_{100,000}

## As a percentage:

24.57879 ≈ 2,457.88%

## As equivalent fractions:

24.57879 = ^{2,457,879}/_{100,000} = ^{9,831,516}/_{400,000} = ^{17,205,153}/_{700,000}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator