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

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

Convert the decimal number 101.694. 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 Jun 06 19:52 UTC (GMT)
Convert the decimal number 4.7. 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 Jun 06 12:54 UTC (GMT)
Convert the decimal number 4.7. 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 Jun 06 11:33 UTC (GMT)
Convert the decimal number 4.7. 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 Jun 06 11:32 UTC (GMT)
Convert the decimal number 4.7. 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 Jun 06 11:32 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 10:52 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 09:17 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 09:17 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 09:16 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 09:10 UTC (GMT)
Convert the decimal number 0.49. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 09:09 UTC (GMT)
Convert the decimal number 0.97657. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 07:27 UTC (GMT)
Convert the decimal number 0.97657. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding Jun 06 07:22 UTC (GMT)
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:

  • 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 reduce 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

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