Convert the pure repeating (recurring) decimal number 6.6666669. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator

Convert 6.6666669 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.

6.6666669 ≈ 6.6666669666667


Multiply the number by 100/100.

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

6.6666669666667 =

6.6666669666667 × 100/100 =

(6.6666669666667 × 100)/100 =

666.66669666667/100 =

666.66669666667% ≈

666.67%

(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, %
  • 6.6666669 ≈ 666.67%

» Convert fractions to percentages, online calculator


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

  • 6.6666669 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 = 6.6666669


Set up the second equation.

  • Number of decimal places repeating: 7

  • Multiply both sides of the first equation by 107 = 10,000,000


y = 6.6666669

10,000,000 × y = 10,000,000 × 6.6666669

10,000,000 × y = 66,666,669.6666669


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.

10,000,000 × y - y = 66,666,669.6666669 - 6.6666669 ⇒

(10,000,000 - 1) × y = 66,666,669.6666669 - 6.6666669 ⇒

We now have a new equation:

9,999,999 × y = 66,666,663


Solve for y in the new equation.

9,999,999 × y = 66,666,663 ⇒

y = 66,666,663/9,999,999

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 6.6666669

According to our calculations:

y = 66,666,663/9,999,999

⇒ 6.6666669 = 66,666,663/9,999,999


3. Reduce (simplify) the fraction above:
66,666,663/9,999,999
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).

66,666,663 = 32 × 7 × 373 × 2,837

9,999,999 = 32 × 239 × 4,649


» 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 (32 × 7 × 373 × 2,837; 32 × 239 × 4,649) = 32


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


Divide both the numerator and the denominator by their GCF.

66,666,663/9,999,999 =

(32 × 7 × 373 × 2,837)/(32 × 239 × 4,649) =

((32 × 7 × 373 × 2,837) ÷ 32) / ((32 × 239 × 4,649) ÷ 32) =

(7 × 373 × 2,837)/(239 × 4,649) =

7,407,407/1,111,111


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.

7,407,407 ÷ 1,111,111 = 6, remainder = 740,741 ⇒

7,407,407 = 6 × 1,111,111 + 740,741 ⇒

7,407,407/1,111,111 =

(6 × 1,111,111 + 740,741) / 1,111,111 =

(6 × 1,111,111) / 1,111,111 + 740,741/1,111,111 =

6 + 740,741/1,111,111 =

6 740,741/1,111,111


7,407,407/1,111,111 ~ 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 5.

7,407,407/1,111,111 = (7,407,407 × 5)/(1,111,111 × 5) = 37,037,035/5,555,555

Example 2. By expanding the fraction by 6.

7,407,407/1,111,111 = (7,407,407 × 6)/(1,111,111 × 6) = 44,444,442/6,666,666

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 7,407,407/1,111,111

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
6.6666669 = 7,407,407/1,111,111

As a mixed number:
6.6666669 = 6 740,741/1,111,111

As a percentage:
6.6666669 ≈ 666.67%

As equivalent fractions:
6.6666669 = 7,407,407/1,111,111 = 37,037,035/5,555,555 = 44,444,442/6,666,666

More operations of this kind

6.666667 = ? Convert the pure repeating (recurring) decimal number 6.666667. 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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