# Convert the decimal number - 0.04. 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 - 0.04

## 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}

#### - 0.04 =

#### - 0.04 × ^{100}/_{100} =

#### - ^{(0.04 × 100)}/_{100} =

#### - ^{4}/_{100} =

#### - 4%

#### In other words:

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

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

#### - 0.04 = - 4%

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

#### - 0.04 can be written as a proper fraction.

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

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

#### - 0.04 = - ^{0.04}/_{1}

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

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

#### This number is: 100.

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

#### - ^{0.04}/_{1} =

#### - ^{(0.04 × 100)}/_{(1 × 100)} =

#### - ^{4}/_{100}

## 3. Reduce (simplify) the fraction above: - ^{4}/_{100}

(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}):

#### 4 = 2^{2}

#### 100 = 2^{2} × 5^{2}

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

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

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

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

#### - ^{4}/_{100} =

#### - ^{22}/_{(22 × 52)} =

#### - ^{(22 ÷ 22)} / _{((22 × 52) ÷ 22)} =

#### - ^{1}/_{52} =

#### - ^{1}/_{25}

## - ^{1}/_{25}: 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 5:

#### - ^{1}/_{25} = - ^{(1 × 5)}/_{(25 × 5)} = - ^{5}/_{125}

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

#### - ^{1}/_{25} = - ^{(1 × 7)}/_{(25 × 7)} = - ^{7}/_{175}

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

#### ... to the initial fraction: - ^{1}/_{25}

## :: Final answer ::

Written in 3 different ways

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

- 0.04 = - ^{1}/_{25}

## As a percentage:

- 0.04 = - 4%

## As equivalent fractions:

- 0.04 = - ^{1}/_{25} = - ^{5}/_{125} = - ^{7}/_{175}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator