Convert the mixed repeating (recurring) decimal number 0.333333338. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Equivalent fractions calculator

Convert 0.333333338 into equivalent fractions and write it as a percentage value

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

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

0.333333338 ≈ 0.33333333833333


Multiply the number by 100/100.

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

0.33333333833333 =

0.33333333833333 × 100/100 =

(0.33333333833333 × 100)/100 =

33.333333833333/100 =

33.333333833333% ≈

33.33%

(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, %
  • 0.333333338 ≈ 33.33%

» Convert fractions to percentages, online calculator


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

  • 0.333333338 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 = 0.333333338


Set up the second equation.

  • Number of decimal places repeating: 8

  • Multiply both sides of the first equation by 108 = 100,000,000


y = 0.333333338

100,000,000 × y = 100,000,000 × 0.333333338

100,000,000 × y = 33,333,333.833333338


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.

100,000,000 × y - y = 33,333,333.833333338 - 0.333333338 ⇒

(100,000,000 - 1) × y = 33,333,333.833333338 - 0.333333338 ⇒

We now have a new equation:

99,999,999 × y = 33,333,333.5


Solve for y in the new equation.

99,999,999 × y = 33,333,333.5 ⇒

y = 33,333,333.5/99,999,999

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 0.333333338

According to our calculations:

y = 33,333,333.5/99,999,999

⇒ 0.333333338 = 33,333,333.5/99,999,999


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.

0.333333338 = (33,333,333.5 × 10)/(99,999,999 × 10)

0.333333338 = 333,333,335/999,999,990


3. Reduce (simplify) the fraction above:
333,333,335/999,999,990
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).

333,333,335 = 5 × 66,666,667

999,999,990 = 2 × 32 × 5 × 11 × 73 × 101 × 137


» 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 (5 × 66,666,667; 2 × 32 × 5 × 11 × 73 × 101 × 137) = 5


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


Divide both the numerator and the denominator by their GCF.

333,333,335/999,999,990 =

(5 × 66,666,667)/(2 × 32 × 5 × 11 × 73 × 101 × 137) =

((5 × 66,666,667) ÷ 5) / ((2 × 32 × 5 × 11 × 73 × 101 × 137) ÷ 5) =

66,666,667/(2 × 32 × 11 × 73 × 101 × 137) =

66,666,667/199,999,998


66,666,667/199,999,998 ~ 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.

66,666,667/199,999,998 = (66,666,667 × 6)/(199,999,998 × 6) = 400,000,002/1,199,999,988

Example 2. By expanding the fraction by 9.

66,666,667/199,999,998 = (66,666,667 × 9)/(199,999,998 × 9) = 600,000,003/1,799,999,982

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 66,666,667/199,999,998

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.333333338 = 66,666,667/199,999,998

As a percentage:
0.333333338 ≈ 33.33%

As equivalent fractions:
0.333333338 = 66,666,667/199,999,998 = 400,000,002/1,199,999,988 = 600,000,003/1,799,999,982

More operations of this kind

0.333333339 = ? Convert the mixed repeating (recurring) decimal number 0.333333339. Turn it into a reduced (simplified) proper fraction 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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