# Convert the decimal number 17.13136. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

## Convert 17.13136

## 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}

#### 17.13136 =

#### 17.13136 × ^{100}/_{100} =

^{(17.13136 × 100)}/_{100} =

#### ^{1,713.136}/_{100} =

#### 1,713.136% ≈

#### 1,713.14%

#### (rounded off to a maximum of 2 decimal places)

#### In other words:

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

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

#### 17.13136 ≈ 1,713.14%

## 2. Write the number as an improper fraction.

#### 17.13136 can be written as an improper fraction.

#### The numerator is larger than or equal to the denominator.

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

#### 17.13136 = ^{17.13136}/_{1}

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

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

#### This number is: 100,000.

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

^{17.13136}/_{1} =

^{(17.13136 × 100,000)}/_{(1 × 100,000)} =

^{1,713,136}/_{100,000}

## 3. Reduce (simplify) the fraction above: ^{1,713,136}/_{100,000}

(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}):

#### 1,713,136 = 2^{4} × 107,071

#### 100,000 = 2^{5} × 5^{5}

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

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

#### GCF (2^{4} × 107,071; 2^{5} × 5^{5}) = 2^{4}

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

^{1,713,136}/_{100,000} =

^{(24 × 107,071)}/_{(25 × 55)} =

^{((24 × 107,071) ÷ 24)} / _{((25 × 55) ÷ 24)} =

^{107,071}/_{(2 × 55)} =

^{107,071}/_{6,250}

## 4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

#### A mixed number = an integer number and a proper fraction, of the same sign.

#### Example 1: 2 ^{1}/_{5}; Example 2: - 1 ^{3}/_{7}.

#### A proper fraction = the numerator is smaller than the denominator.

#### 107,071 ÷ 6,250 = 17, remainder = 821 ⇒

#### 107,071 = 17 × 6,250 + 821 ⇒

#### ^{107,071}/_{6,250} =

#### ^{(17 × 6,250 + 821)} / _{6,250} =

^{(17 × 6,250)} / _{6,250} + ^{821}/_{6,250} =

#### 17 + ^{821}/_{6,250} =

#### 17 ^{821}/_{6,250}

^{107,071}/_{6,250}: 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:

^{107,071}/_{6,250} = ^{(107,071 × 4)}/_{(6,250 × 4)} = ^{428,284}/_{25,000}

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

^{107,071}/_{6,250} = ^{(107,071 × 7)}/_{(6,250 × 7)} = ^{749,497}/_{43,750}

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

#### ... to the initial fraction: ^{107,071}/_{6,250}

## :: Final answer ::

Written in 4 different ways

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

17.13136 = ^{107,071}/_{6,250}

## As a mixed number:

17.13136 = 17 ^{821}/_{6,250}

## As a percentage:

17.13136 ≈ 1,713.14%

## As equivalent fractions:

17.13136 = ^{107,071}/_{6,250} = ^{428,284}/_{25,000} = ^{749,497}/_{43,750}

### More operations of this kind

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