# Convert the mixed repeating (recurring) decimal number 0.94. 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 0.94

## 1. Write the mixed repeating (recurring) decimal number as a percentage.

### Approximate to the desired number of decimal places (14):

#### 0.94 ≈ 0.94444444444444

### Multiply the number by ^{100}/_{100}.

#### The value of the number does not change when multiplying by ^{100}/_{100}.

#### Note: ^{100}/_{100} = 1

#### 0.94444444444444 =

#### 0.94444444444444 × ^{100}/_{100} =

^{(0.94444444444444 × 100)}/_{100} =

#### ^{94.444444444444}/_{100} =

#### 94.444444444444% ≈

#### 94.44%

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

#### In other words:

#### Approximate to the desired number of decimal places...

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

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

#### 0.94 ≈ 94.44%

## 2. Write the mixed repeating (recurring) decimal number as a proper fraction.

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

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

### Set up the first equation.

#### Let y equal the decimal number:

#### y = 0.94

### Set up the second equation.

#### Number of decimal places repeating: 1

#### Multiply both sides of the first equation by 10^{1} = 10

#### y = 0.94

#### 10 × y = 10 × 0.94

#### 10 × y = 9.4

#### Get the same number of decimal places as for y:

#### 10 × y = 9.44

#### Note: 9.44 = 9.4

### Subtract the first equation from the second equation.

#### Having the same number of decimal places ...

#### The repeating pattern drops off by subtracting the two equations.

#### 10 × y - y = 9.44 - 0.94 ⇒

#### (10 - 1) × y = 9.44 - 0.94 ⇒

#### We now have a new equation:

#### 9 × y = 8.5

### Solve for y in the new equation.

#### 9 × y = 8.5 ⇒

#### y = ^{8.5}/_{9}

#### Let the result written as a fraction.

### Write the number as a fraction.

#### According to our first equation:

#### y = 0.94

#### According to our calculations:

#### y = ^{8.5}/_{9}

#### ⇒ 0.94 = ^{8.5}/_{9}

### Get rid of the decimal places in the fraction above.

#### Multiply the top and the bottom number by 10.

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

#### 0.94 = ^{(8.5 × 10)}/_{(9 × 10)}

#### 0.94 = ^{85}/_{90}

## 3. Reduce (simplify) the fraction above: ^{85}/_{90}

(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}):

#### 85 = 5 × 17

#### 90 = 2 × 3^{2} × 5

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

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

#### GCF (5 × 17; 2 × 3^{2} × 5) = 5

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

^{85}/_{90} =

^{(5 × 17)}/_{(2 × 32 × 5)} =

^{((5 × 17) ÷ 5)} / _{((2 × 32 × 5) ÷ 5)} =

^{17}/_{(2 × 32)} =

^{17}/_{18}

^{17}/_{18}: 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:

^{17}/_{18} = ^{(17 × 6)}/_{(18 × 6)} = ^{102}/_{108}

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

^{17}/_{18} = ^{(17 × 9)}/_{(18 × 9)} = ^{153}/_{162}

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

#### ... to the initial fraction: ^{17}/_{18}

## :: Final answer ::

Written in 3 different ways

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

0.94 = ^{17}/_{18}

## As a percentage:

0.94 ≈ 94.44%

## As equivalent fractions:

0.94 = ^{17}/_{18} = ^{102}/_{108} = ^{153}/_{162}

### More operations of this kind

## Decimal numbers to fractions and percentages, calculator