Convert the decimal number 5.85. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage value. Equivalent fractions calculator

Convert 5.85 into equivalent fractions and write it as a percentage value

1. Write the number as a percentage.

  • Multiply the number by 100/100
  • Note: 100/100 = 1
  • The value of the number does not change when multiplying by 100/100

5.85 =

5.85 × 100/100 =

(5.85 × 100)/100 =

585/100 =

585%


  • In other words:
  • Multiply the number by 100...
  • ... And then add the percent sign, %
  • 5.85 = 585%

» Convert fractions to percentages, online calculator


2. Write the number as an improper fraction.

  • 5.85 can be written as an improper fraction.
  • An improper fraction = the numerator is larger than or equal to the denominator..

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

5.85 = 5.85/1


Turn the top number into a whole number.

  • Multiply both the top and the bottom by the same number.
  • This number is: 100.
  • 1 followed by as many 0-s as the number of digits after the decimal point.

5.85/1 =

(5.85 × 100)/(1 × 100) =

585/100


3. Reduce (simplify) the fraction above:
585/100
to the lowest terms, to its simplest equivalent form, irreducible.

To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.


Factor the numerator and denominator (prime factorization).

585 = 32 × 5 × 13

100 = 22 × 52


» 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.

GCF (32 × 5 × 13; 22 × 52) = 5


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


Divide both the numerator and the denominator by their GCF.

585/100 =

(32 × 5 × 13)/(22 × 52) =

((32 × 5 × 13) ÷ 5) / ((22 × 52) ÷ 5) =

(32 × 13)/(22 × 5) =

117/20


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.

117 ÷ 20 = 5, remainder = 17 ⇒

117 = 5 × 20 + 17 ⇒

117/20 =

(5 × 20 + 17) / 20 =

(5 × 20) / 20 + 17/20 =

5 + 17/20 =

5 17/20


117/20 ~ 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.

117/20 = (117 × 2)/(20 × 2) = 234/40

Example 2. By expanding the fraction by 6.

117/20 = (117 × 6)/(20 × 6) = 702/120

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 117/20

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
5.85 = 117/20

As a mixed number:
5.85 = 5 17/20

As a percentage:
5.85 = 585%

As equivalent fractions:
5.85 = 117/20 = 234/40 = 702/120

More operations of this kind

5.86 = ? Convert the decimal number 5.86. 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

Decimal numbers to fractions and percentages, calculator

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.

More on ordinary (common) fractions / theory: