# Convert the decimal number 1.1765. 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 1.1765

## 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}

#### 1.1765 =

#### 1.1765 × ^{100}/_{100} =

^{(1.1765 × 100)}/_{100} =

#### ^{117.65}/_{100} =

#### 117.65%

#### In other words:

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

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

#### 1.1765 = 117.65%

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

#### 1.1765 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:

#### 1.1765 = ^{1.1765}/_{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.

^{1.1765}/_{1} =

^{(1.1765 × 10,000)}/_{(1 × 10,000)} =

^{11,765}/_{10,000}

## 3. Reduce (simplify) the fraction above: ^{11,765}/_{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}):

#### 11,765 = 5 × 13 × 181

#### 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 × 13 × 181; 2^{4} × 5^{4}) = 5

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

^{11,765}/_{10,000} =

^{(5 × 13 × 181)}/_{(24 × 54)} =

^{((5 × 13 × 181) ÷ 5)} / _{((24 × 54) ÷ 5)} =

^{(13 × 181)}/_{(24 × 53)} =

^{2,353}/_{2,000}

## 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.

#### 2,353 ÷ 2,000 = 1, remainder = 353 ⇒

#### 2,353 = 1 × 2,000 + 353 ⇒

#### ^{2,353}/_{2,000} =

#### ^{(1 × 2,000 + 353)} / _{2,000} =

^{(1 × 2,000)} / _{2,000} + ^{353}/_{2,000} =

#### 1 + ^{353}/_{2,000} =

#### 1 ^{353}/_{2,000}

^{2,353}/_{2,000}: 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 6:

^{2,353}/_{2,000} = ^{(2,353 × 6)}/_{(2,000 × 6)} = ^{14,118}/_{12,000}

### Example 2. By expanding the fraction by 10:

^{2,353}/_{2,000} = ^{(2,353 × 10)}/_{(2,000 × 10)} = ^{23,530}/_{20,000}

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

#### ... to the initial fraction: ^{2,353}/_{2,000}

## :: Final answer ::

Written in 4 different ways

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

1.1765 = ^{2,353}/_{2,000}

## As a mixed number:

1.1765 = 1 ^{353}/_{2,000}

## As a percentage:

1.1765 = 117.65%

## As equivalent fractions:

1.1765 = ^{2,353}/_{2,000} = ^{14,118}/_{12,000} = ^{23,530}/_{20,000}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator