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

Decimal numbers to fractions and percentages, calculator

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All the integers, terminating and repeating (recurring) decimal numbers converted to fractions, mixed numbers 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:

2. How to write the number as a fraction:

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:

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


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


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


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers