Convert integers, terminating and repeating (recurring) decimal numbers to fractions and percentages. If the decimal numbers are larger than 1 they are also turned into mixed numbers. Equivalent fractions calculator

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Decimal numbers to fractions and percentages, calculator

The latest integers, terminating and repeating (recurring) decimal numbers converted to fractions and turned into percentages

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.

Example: Convert the decimal number 3.45. 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

1. Write the number as a percentage.

Note: 100/100 = 1

3.45 = 3.45 × 100/100 = (3.45 × 100)/100 = 345/100 = 345%

In other words: multiply the number by 100... and then add the percent sign, %: 3.45 = 345%


2. Write the number as an improper fraction.

(The numerator is larger than or equal to the denominator).

Write down the number divided by 1, as a fraction:

3.45 = 3.45/1

Turn the top number into a whole number.

Multiply both the top and the bottom by the same number: 100 (1 followed by as many 0s as the number of digits after the decimal point).


3.45/1 = (3.45 × 100)/(1 × 100) = 345/100

3. Reduce (simplify) the fraction above: 345/100
(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).

345 = 3 × 5 × 23; 100 = 22 × 52;


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

Multiply all the common prime factors by the lowest exponents.


GCF (3 × 5 × 23; 22 × 52) = 5


Divide both the numerator and the denominator by their greatest common factor, GCF.

345/100 = (3 × 5 × 23)/(22 × 52) = ((3 × 5 × 23) ÷ 5) / ((22 × 52) ÷ 5) = (3 × 23)/(22 × 5) = 69/20


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.


69 ÷ 20 = 3, remainder = 9 => 69 = 3 × 20 + 9 =>


69/20 = (3 × 20 + 9) / 20 = (3 × 20) / 20 + 9/20 = 3 + 9/20 = 3 9/20


69/20: Equivalent fractions.

By expanding the reduced fraction we can build up equivalent fractions (multiply the numerator & the denominator by the same number).


Example 1. By expanding the fraction by 2:

69/20 = (69 × 2)/(20 × 2) = 138/40

Example 2. By expanding the fraction by 6:

69/20 = (69 × 6)/(20 × 6) = 414/120

Of course, the above fractions are reducing... to the initial fraction: 69/20

:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
3.45 = 69/20

As a mixed number:
3.45 = 3 9/20

As a percentage:
3.45 = 345%

As equivalent fractions:
3.45 = 69/20 = 138/40 = 414/120

More on ordinary (common) fractions / theory: