Convert the pure repeating (recurring) decimal number 6.84. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator

Convert 6.84 into equivalent fractions and write it as a percentage value

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

Approximate to the desired number of decimal places (14).

6.84 ≈ 6.84848484848485


Multiply the number by 100/100.

  • The value of the number does not change when multiplying by 100/100.
  • Note: 100/100 = 1

6.84848484848485 =

6.84848484848485 × 100/100 =

(6.84848484848485 × 100)/100 =

684.848484848485/100 =

684.848484848485% ≈

684.85%

(rounded off to max. 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, %
  • 6.84 ≈ 684.85%

» Convert fractions to percentages, online calculator


2. Write the pure repeating (recurring) decimal number as an improper fraction.

  • 6.84 can be written as an improper fraction.

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

Set up the first equation.

  • Let y equal the decimal number:

  • y = 6.84


Set up the second equation.

  • Number of decimal places repeating: 2

  • Multiply both sides of the first equation by 102 = 100


y = 6.84

100 × y = 100 × 6.84

100 × y = 684.84


Subtract the first equation from the second one.

  • Having the same number of decimal places ...
  • The repeating pattern drops off by subtracting the two equations.

100 × y - y = 684.84 - 6.84 ⇒

(100 - 1) × y = 684.84 - 6.84 ⇒

We now have a new equation:

99 × y = 678


Solve for y in the new equation.

99 × y = 678 ⇒

y = 678/99

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 6.84

According to our calculations:

y = 678/99

⇒ 6.84 = 678/99


3. Reduce (simplify) the fraction above:
678/99
to the lowest terms, to its simplest equivalent form, irreducible.

To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.


Factor the numerator and denominator (prime factorization).

678 = 2 × 3 × 113

99 = 32 × 11


» Prime factorization: break numbers down to prime factors, online calculator


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

Multiply all the common prime factors by the lowest exponents.

GCF (2 × 3 × 113; 32 × 11) = 3


» Calculate the greatest (highest) common factor (divisor), GCF, online calculator


Divide both the numerator and the denominator by their GCF.

678/99 =

(2 × 3 × 113)/(32 × 11) =

((2 × 3 × 113) ÷ 3) / ((32 × 11) ÷ 3) =

(2 × 113)/(3 × 11) =

226/33


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.

226 ÷ 33 = 6, remainder = 28 ⇒

226 = 6 × 33 + 28 ⇒

226/33 =

(6 × 33 + 28) / 33 =

(6 × 33) / 33 + 28/33 =

6 + 28/33 =

6 28/33


226/33 ~ 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 2.

226/33 = (226 × 2)/(33 × 2) = 452/66

Example 2. By expanding the fraction by 6.

226/33 = (226 × 6)/(33 × 6) = 1,356/198

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 226/33

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
6.84 = 226/33

As a mixed number:
6.84 = 6 28/33

As a percentage:
6.84 ≈ 684.85%

As equivalent fractions:
6.84 = 226/33 = 452/66 = 1,356/198

More operations of this kind

6.85 = ? Convert the pure repeating (recurring) decimal number 6.85. 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

Decimal numbers to fractions and percentages, calculator

Learn how to turn a decimal number into a fraction and a percentage. Steps.

1. How to write the number as a percentage:

  • Multiply the number by 100. Then add the percent sign, %.

2. How to write the number as a fraction:

  • Write down the number divided by 1, as a fraction.
  • Turn the top number into a whole number: multiply both the top and the bottom by the same number.
  • Reduce (simplify) the above fraction 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.
  • If the fraction is an improper one, rewrite it as a mixed number (mixed fraction).
  • Calculate equivalent fractions. By expanding it we can build up equivalent fractions: multiply the numerator & the denominator by the same number.

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