# Convert the decimal number 0.075. 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 0.075

## 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}

#### 0.075 =

#### 0.075 × ^{100}/_{100} =

^{(0.075 × 100)}/_{100} =

#### ^{7.5}/_{100} =

#### 7.5%

#### In other words:

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

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

#### 0.075 = 7.5%

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

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

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

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

#### 0.075 = ^{0.075}/_{1}

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

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

#### This number is: 1,000.

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

^{0.075}/_{1} =

^{(0.075 × 1,000)}/_{(1 × 1,000)} =

^{75}/_{1,000}

## 3. Reduce (simplify) the fraction above: ^{75}/_{1,000}

(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}):

#### 75 = 3 × 5^{2}

#### 1,000 = 2^{3} × 5^{3}

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

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

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

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

^{75}/_{1,000} =

^{(3 × 52)}/_{(23 × 53)} =

^{((3 × 52) ÷ 52)} / _{((23 × 53) ÷ 52)} =

^{3}/_{(23 × 5)} =

^{3}/_{40}

^{3}/_{40}: 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:

^{3}/_{40} = ^{(3 × 4)}/_{(40 × 4)} = ^{12}/_{160}

### Example 2. By expanding the fraction by 5:

^{3}/_{40} = ^{(3 × 5)}/_{(40 × 5)} = ^{15}/_{200}

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

#### ... to the initial fraction: ^{3}/_{40}

## :: Final answer ::

Written in 3 different ways

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

0.075 = ^{3}/_{40}

## As a percentage:

0.075 = 7.5%

## As equivalent fractions:

0.075 = ^{3}/_{40} = ^{12}/_{160} = ^{15}/_{200}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator