Convert the mixed repeating (recurring) decimal number 1.584. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator

Convert 1.584 into equivalent fractions and write it as a percentage value

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

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

1.584 ≈ 1.58444444444444


Multiply the number by 100/100.

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

1.58444444444444 =

1.58444444444444 × 100/100 =

(1.58444444444444 × 100)/100 =

158.444444444444/100 =

158.444444444444% ≈

158.44%

(rounded off to max. 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, %
  • 1.584 ≈ 158.44%

» Convert fractions to percentages, online calculator


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

  • 1.584 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 = 1.584


Set up the second equation.

  • Number of decimal places repeating: 1

  • Multiply both sides of the first equation by 101 = 10


y = 1.584

10 × y = 10 × 1.584

10 × y = 15.84

Get the same number of decimal places as for y:

10 × y = 15.844

Note: 15.844 = 15.84


Subtract the first equation from the second one.

  • Having the same number of decimal places ...
  • The repeating pattern drops off by subtracting the two equations.

10 × y - y = 15.844 - 1.584 ⇒

(10 - 1) × y = 15.844 - 1.584 ⇒

We now have a new equation:

9 × y = 14.26


Solve for y in the new equation.

9 × y = 14.26 ⇒

y = 14.26/9

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 1.584

According to our calculations:

y = 14.26/9

⇒ 1.584 = 14.26/9


Get rid of the decimal places in the fraction above.

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

1.584 = (14.26 × 100)/(9 × 100)

1.584 = 1,426/900


3. Reduce (simplify) the fraction above:
1,426/900
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).

1,426 = 2 × 23 × 31

900 = 22 × 32 × 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 (2 × 23 × 31; 22 × 32 × 52) = 2


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


Divide both the numerator and the denominator by their GCF.

1,426/900 =

(2 × 23 × 31)/(22 × 32 × 52) =

((2 × 23 × 31) ÷ 2) / ((22 × 32 × 52) ÷ 2) =

(23 × 31)/(2 × 32 × 52) =

713/450


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.

713 ÷ 450 = 1, remainder = 263 ⇒

713 = 1 × 450 + 263 ⇒

713/450 =

(1 × 450 + 263) / 450 =

(1 × 450) / 450 + 263/450 =

1 + 263/450 =

1 263/450


713/450 ~ 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 4.

713/450 = (713 × 4)/(450 × 4) = 2,852/1,800

Example 2. By expanding the fraction by 6.

713/450 = (713 × 6)/(450 × 6) = 4,278/2,700

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 713/450

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
1.584 = 713/450

As a mixed number:
1.584 = 1 263/450

As a percentage:
1.584 ≈ 158.44%

As equivalent fractions:
1.584 = 713/450 = 2,852/1,800 = 4,278/2,700

More operations of this kind

1.585 = ? Convert the mixed repeating (recurring) decimal number 1.585. 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.

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