Convert the pure repeating (recurring) decimal number 0.315. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Equivalent fractions calculator

Convert 0.315 into equivalent fractions and write it as a percentage value

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

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

0.315 ≈ 0.31531531531532


Multiply the number by 100/100.

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

0.31531531531532 =

0.31531531531532 × 100/100 =

(0.31531531531532 × 100)/100 =

31.531531531532/100 =

31.531531531532% ≈

31.53%

(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, %
  • 0.315 ≈ 31.53%

» Convert fractions to percentages, online calculator


2. Write the pure repeating (recurring) decimal number as a proper fraction.

  • 0.315 can be written as a proper fraction.

  • The numerator is smaller than the denominator.

Set up the first equation.

  • Let y equal the decimal number:

  • y = 0.315


Set up the second equation.

  • Number of decimal places repeating: 3

  • Multiply both sides of the first equation by 103 = 1,000


y = 0.315

1,000 × y = 1,000 × 0.315

1,000 × y = 315.315


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.

1,000 × y - y = 315.315 - 0.315 ⇒

(1,000 - 1) × y = 315.315 - 0.315 ⇒

We now have a new equation:

999 × y = 315


Solve for y in the new equation.

999 × y = 315 ⇒

y = 315/999

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 0.315

According to our calculations:

y = 315/999

⇒ 0.315 = 315/999


3. Reduce (simplify) the fraction above:
315/999
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).

315 = 32 × 5 × 7

999 = 33 × 37


» 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 × 7; 33 × 37) = 32


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


Divide both the numerator and the denominator by their GCF.

315/999 =

(32 × 5 × 7)/(33 × 37) =

((32 × 5 × 7) ÷ 32) / ((33 × 37) ÷ 32) =

(5 × 7)/(3 × 37) =

35/111


35/111 ~ 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.

35/111 = (35 × 4)/(111 × 4) = 140/444

Example 2. By expanding the fraction by 8.

35/111 = (35 × 8)/(111 × 8) = 280/888

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 35/111

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.315 = 35/111

As a percentage:
0.315 ≈ 31.53%

As equivalent fractions:
0.315 = 35/111 = 140/444 = 280/888

More operations of this kind

0.316 = ? Convert the pure repeating (recurring) decimal number 0.316. Turn it into a reduced (simplified) proper fraction 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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