Convert the pure repeating (recurring) decimal number 2.34. 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

Convert 2.34

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

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


2.342.34343434343434


Multiply the number by 100/100.

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

Note: 100/100 = 1

2.34343434343434 =


2.34343434343434 × 100/100 =


(2.34343434343434 × 100)/100 =


234.343434343434/100 =


234.343434343434% ≈


234.34%


(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, %


2.34234.34%


Convert fractions to percentages, online calculator


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

2.34 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 = 2.34


Set up the second equation.

Number of decimal places repeating: 2

Multiply both sides of the first equation by 102 = 100

y = 2.34


100 × y = 100 × 2.34


100 × y = 234.34


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.

100 × y - y = 234.34 - 2.34 =>


(100 - 1) × y = 234.34 - 2.34 =>


We now have a new equation:


99 × y = 232


Solve for y in the new equation.

99 × y = 232 =>


y = 232/99

Let the result written down as a fraction.


Write the number as a fraction.

According to our first equation:


y = 2.34


According to our calculations:


y = 232/99


=> 2.34 = 232/99


3. Reduce (simplify) the fraction above: 232/99
(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):


232 = 23 × 29


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.


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


GCF (23 × 29; 32 × 11) = 1

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



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

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.


232 ÷ 99 = 2, remainder = 34 =>


232 = 2 × 99 + 34 =>


232/99 =


(2 × 99 + 34) / 99 =


(2 × 99) / 99 + 34/99 =


2 + 34/99 =


2 34/99


232/99: Equivalent fractions.

The above fraction cannot be reduced.


That is, it has the smallest numerator and denominator possible.


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 3:

232/99 = (232 × 3)/(99 × 3) = 696/297

Example 2. By expanding the fraction by 5:

232/99 = (232 × 5)/(99 × 5) = 1,160/495

Of course, the above fractions are reducing...


... to the initial fraction: 232/99


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
2.34 = 232/99

As a mixed number:
2.34 = 2 34/99

As a percentage:
2.34 ≈ 234.34%

As equivalent fractions:
2.34 = 232/99 = 696/297 = 1,160/495

More operations of this kind:

2.35 = ?

Decimal numbers to fractions and percentages, calculator

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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:

2. How to write the number as a fraction:

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers