# Convert the decimal number 0.45. 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 0.45

## 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}

#### 0.45 =

#### 0.45 × ^{100}/_{100} =

^{(0.45 × 100)}/_{100} =

#### ^{45}/_{100} =

#### 45%

#### In other words:

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

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

#### 0.45 = 45%

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

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

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

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

#### 0.45 = ^{0.45}/_{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.

^{0.45}/_{1} =

^{(0.45 × 100)}/_{(1 × 100)} =

^{45}/_{100}

## 3. Reduce (simplify) the fraction above: ^{45}/_{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}):

#### 45 = 3^{2} × 5

#### 100 = 2^{2} × 5^{2}

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

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

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

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

^{45}/_{100} =

^{(32 × 5)}/_{(22 × 52)} =

^{((32 × 5) ÷ 5)} / _{((22 × 52) ÷ 5)} =

^{32}/_{(22 × 5)} =

^{9}/_{20}

^{9}/_{20}: 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 6:

^{9}/_{20} = ^{(9 × 6)}/_{(20 × 6)} = ^{54}/_{120}

### Example 2. By expanding the fraction by 9:

^{9}/_{20} = ^{(9 × 9)}/_{(20 × 9)} = ^{81}/_{180}

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

#### ... to the initial fraction: ^{9}/_{20}

## :: Final answer ::

Written in 3 different ways

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

0.45 = ^{9}/_{20}

## As a percentage:

0.45 = 45%

## As equivalent fractions:

0.45 = ^{9}/_{20} = ^{54}/_{120} = ^{81}/_{180}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator