Convert the pure repeating (recurring) decimal number 0.166666668. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Equivalent fractions calculator

Convert 0.166666668 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).

0.166666668 ≈ 0.16666666816667


Multiply the number by 100/100.

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

0.16666666816667 =

0.16666666816667 × 100/100 =

(0.16666666816667 × 100)/100 =

16.666666816667/100 =

16.666666816667% ≈

16.67%

(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, %
  • 0.166666668 ≈ 16.67%

» Convert fractions to percentages, online calculator


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

  • 0.166666668 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 = 0.166666668


Set up the second equation.

  • Number of decimal places repeating: 9

  • Multiply both sides of the first equation by 109 = 1,000,000,000


y = 0.166666668

1,000,000,000 × y = 1,000,000,000 × 0.166666668

1,000,000,000 × y = 166,666,668.166666668


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.

1,000,000,000 × y - y = 166,666,668.166666668 - 0.166666668 ⇒

(1,000,000,000 - 1) × y = 166,666,668.166666668 - 0.166666668 ⇒

We now have a new equation:

999,999,999 × y = 166,666,668


Solve for y in the new equation.

999,999,999 × y = 166,666,668 ⇒

y = 166,666,668/999,999,999

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 0.166666668

According to our calculations:

y = 166,666,668/999,999,999

⇒ 0.166666668 = 166,666,668/999,999,999


3. Reduce (simplify) the fraction above:
166,666,668/999,999,999
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).

166,666,668 = 22 × 3 × 7 × 1092 × 167

999,999,999 = 34 × 37 × 333,667


» 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 (22 × 3 × 7 × 1092 × 167; 34 × 37 × 333,667) = 3


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


Divide both the numerator and the denominator by their GCF.

166,666,668/999,999,999 =

(22 × 3 × 7 × 1092 × 167)/(34 × 37 × 333,667) =

((22 × 3 × 7 × 1092 × 167) ÷ 3) / ((34 × 37 × 333,667) ÷ 3) =

(22 × 7 × 1092 × 167)/(33 × 37 × 333,667) =

55,555,556/333,333,333


55,555,556/333,333,333 ~ 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 4.

55,555,556/333,333,333 = (55,555,556 × 4)/(333,333,333 × 4) = 222,222,224/1,333,333,332

Example 2. By expanding the fraction by 6.

55,555,556/333,333,333 = (55,555,556 × 6)/(333,333,333 × 6) = 333,333,336/1,999,999,998

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 55,555,556/333,333,333

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.166666668 = 55,555,556/333,333,333

As a percentage:
0.166666668 ≈ 16.67%

As equivalent fractions:
0.166666668 = 55,555,556/333,333,333 = 222,222,224/1,333,333,332 = 333,333,336/1,999,999,998

More operations of this kind

0.166666669 = ? Convert the pure repeating (recurring) decimal number 0.166666669. 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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