# Convert the decimal number 0.6462. 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 0.6462

## 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}

#### 0.6462 =

#### 0.6462 × ^{100}/_{100} =

^{(0.6462 × 100)}/_{100} =

#### ^{64.62}/_{100} =

#### 64.62%

#### In other words:

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

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

#### 0.6462 = 64.62%

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

#### 0.6462 can be written as a proper fraction.

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

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

#### 0.6462 = ^{0.6462}/_{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.

^{0.6462}/_{1} =

^{(0.6462 × 10,000)}/_{(1 × 10,000)} =

^{6,462}/_{10,000}

## 3. Reduce (simplify) the fraction above: ^{6,462}/_{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}):

#### 6,462 = 2 × 3^{2} × 359

#### 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 (2 × 3^{2} × 359; 2^{4} × 5^{4}) = 2

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

^{6,462}/_{10,000} =

^{(2 × 32 × 359)}/_{(24 × 54)} =

^{((2 × 32 × 359) ÷ 2)} / _{((24 × 54) ÷ 2)} =

^{(32 × 359)}/_{(23 × 54)} =

^{3,231}/_{5,000}

^{3,231}/_{5,000}: 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 3:

^{3,231}/_{5,000} = ^{(3,231 × 3)}/_{(5,000 × 3)} = ^{9,693}/_{15,000}

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

^{3,231}/_{5,000} = ^{(3,231 × 7)}/_{(5,000 × 7)} = ^{22,617}/_{35,000}

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

#### ... to the initial fraction: ^{3,231}/_{5,000}

## :: Final answer ::

Written in 3 different ways

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

0.6462 = ^{3,231}/_{5,000}

## As a percentage:

0.6462 = 64.62%

## As equivalent fractions:

0.6462 = ^{3,231}/_{5,000} = ^{9,693}/_{15,000} = ^{22,617}/_{35,000}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator