# Convert the decimal number 0.0625. 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 0.0625

## 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}

#### 0.0625 =

#### 0.0625 × ^{100}/_{100} =

^{(0.0625 × 100)}/_{100} =

#### ^{6.25}/_{100} =

#### 6.25%

#### In other words:

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

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

#### 0.0625 = 6.25%

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

#### 0.0625 can be written as a proper fraction.

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

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

#### 0.0625 = ^{0.0625}/_{1}

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

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

#### This number is: 10,000.

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

^{0.0625}/_{1} =

^{(0.0625 × 10,000)}/_{(1 × 10,000)} =

^{625}/_{10,000}

## 3. Reduce (simplify) the fraction above: ^{625}/_{10,000}

(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}):

#### 625 = 5^{4}

#### 10,000 = 2^{4} × 5^{4}

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

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

#### GCF (5^{4}; 2^{4} × 5^{4}) = 5^{4}

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

^{625}/_{10,000} =

^{54}/_{(24 × 54)} =

^{(54 ÷ 54)} / _{((24 × 54) ÷ 54)} =

^{1}/_{24} =

^{1}/_{16}

^{1}/_{16}: 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 3:

^{1}/_{16} = ^{(1 × 3)}/_{(16 × 3)} = ^{3}/_{48}

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

^{1}/_{16} = ^{(1 × 7)}/_{(16 × 7)} = ^{7}/_{112}

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

#### ... to the initial fraction: ^{1}/_{16}

## :: Final answer ::

Written in 3 different ways

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

0.0625 = ^{1}/_{16}

## As a percentage:

0.0625 = 6.25%

## As equivalent fractions:

0.0625 = ^{1}/_{16} = ^{3}/_{48} = ^{7}/_{112}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator