# Convert the decimal number 0.27445. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

## Convert 0.27445

## 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}

#### 0.27445 =

#### 0.27445 × ^{100}/_{100} =

^{(0.27445 × 100)}/_{100} =

#### ^{27.445}/_{100} =

#### 27.445% ≈

#### 27.45%

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

#### In other words:

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

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

#### 0.27445 ≈ 27.45%

## 2. Write the number as a proper fraction.

#### 0.27445 can be written as a proper fraction.

#### The numerator is smaller than the denominator.

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

#### 0.27445 = ^{0.27445}/_{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.

^{0.27445}/_{1} =

^{(0.27445 × 100,000)}/_{(1 × 100,000)} =

^{27,445}/_{100,000}

## 3. Reduce (simplify) the fraction above: ^{27,445}/_{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}):

#### 27,445 = 5 × 11 × 499

#### 100,000 = 2^{5} × 5^{5}

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

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

#### GCF (5 × 11 × 499; 2^{5} × 5^{5}) = 5

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

^{27,445}/_{100,000} =

^{(5 × 11 × 499)}/_{(25 × 55)} =

^{((5 × 11 × 499) ÷ 5)} / _{((25 × 55) ÷ 5)} =

^{(11 × 499)}/_{(25 × 54)} =

^{5,489}/_{20,000}

^{5,489}/_{20,000}: 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:

^{5,489}/_{20,000} = ^{(5,489 × 4)}/_{(20,000 × 4)} = ^{21,956}/_{80,000}

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

^{5,489}/_{20,000} = ^{(5,489 × 7)}/_{(20,000 × 7)} = ^{38,423}/_{140,000}

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

#### ... to the initial fraction: ^{5,489}/_{20,000}

## :: Final answer ::

Written in 3 different ways

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

0.27445 = ^{5,489}/_{20,000}

## As a percentage:

0.27445 ≈ 27.45%

## As equivalent fractions:

0.27445 = ^{5,489}/_{20,000} = ^{21,956}/_{80,000} = ^{38,423}/_{140,000}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator