Convert the mixed repeating (recurring) decimal number 0.12903. 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 0.12903

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

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

0.129030.12903333333333


Multiply the number by 100/100.

The value of the number does not change when multiplying by 100/100.

Note: 100/100 = 1


0.12903333333333 =


0.12903333333333 × 100/100 =


(0.12903333333333 × 100)/100 =


12.903333333333/100 =


12.903333333333% ≈


12.9%


(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, %


0.1290312.9%



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

0.12903 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 = 0.12903


Set up the second equation.

Number of decimal places repeating: 1

Multiply both sides of the first equation by 101 = 10


y = 0.12903


10 × y = 10 × 0.12903


10 × y = 1.2903


Get the same number of decimal places as for y:


10 × y = 1.29033


Note: 1.29033 = 1.2903


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 = 1.29033 - 0.12903


(10 - 1) × y = 1.29033 - 0.12903


We now have a new equation:


9 × y = 1


Solve for y in the new equation.

9 × y = 1 ⇒


y = 1/9


Let the result written as a fraction.



Write the number as a fraction.

According to our first equation:

y = 0.12903


According to our calculations:

y = 1/9


⇒ 0.12903 = 1/9


3. Reduce (simplify) the fraction above: 1/9
(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 (an):


1 = one


9 = 32



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

Multiply all the common prime factors by the lowest exponents.

But, the numerator and the denominator have no common factors.


GCF (one; 32) = 1




The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.


1/9: 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:

1/9 = (1 × 2)/(9 × 2) = 2/18

Example 2. By expanding the fraction by 6:

1/9 = (1 × 6)/(9 × 6) = 6/54

Of course, the above fractions are reducing...


... to the initial fraction: 1/9



:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.12903 = 1/9

As a percentage:
0.12903 ≈ 12.9%

As equivalent fractions:
0.12903 = 1/9 = 2/18 = 6/54

More operations of this kind

0.12904 = ? Convert the mixed repeating (recurring) decimal number 0.12904. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

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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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