# Convert the decimal number 68.4. 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 68.4

## 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}

#### 68.4 =

#### 68.4 × ^{100}/_{100} =

^{(68.4 × 100)}/_{100} =

#### ^{6,840}/_{100} =

#### 6,840%

#### In other words:

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

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

#### 68.4 = 6,840%

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

#### 68.4 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:

#### 68.4 = ^{68.4}/_{1}

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

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

#### This number is: 10.

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

^{68.4}/_{1} =

^{(68.4 × 10)}/_{(1 × 10)} =

^{684}/_{10}

## 3. Reduce (simplify) the fraction above: ^{684}/_{10}

(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}):

#### 684 = 2^{2} × 3^{2} × 19

#### 10 = 2 × 5

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

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

#### GCF (2^{2} × 3^{2} × 19; 2 × 5) = 2

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

^{684}/_{10} =

^{(22 × 32 × 19)}/_{(2 × 5)} =

^{((22 × 32 × 19) ÷ 2)} / _{((2 × 5) ÷ 2)} =

^{(2 × 32 × 19)}/_{5} =

^{342}/_{5}

## 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.

#### 342 ÷ 5 = 68, remainder = 2 ⇒

#### 342 = 68 × 5 + 2 ⇒

#### ^{342}/_{5} =

#### ^{(68 × 5 + 2)} / _{5} =

^{(68 × 5)} / _{5} + ^{2}/_{5} =

#### 68 + ^{2}/_{5} =

#### 68 ^{2}/_{5}

^{342}/_{5}: 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:

^{342}/_{5} = ^{(342 × 4)}/_{(5 × 4)} = ^{1,368}/_{20}

### Example 2. By expanding the fraction by 8:

^{342}/_{5} = ^{(342 × 8)}/_{(5 × 8)} = ^{2,736}/_{40}

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

#### ... to the initial fraction: ^{342}/_{5}

## :: Final answer ::

Written in 4 different ways

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

68.4 = ^{342}/_{5}

## As a mixed number:

68.4 = 68 ^{2}/_{5}

## As a percentage:

68.4 = 6,840%

## As equivalent fractions:

68.4 = ^{342}/_{5} = ^{1,368}/_{20} = ^{2,736}/_{40}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator