Convert the mixed repeating (recurring) decimal number 1.216. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator

Convert 1.216 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).

1.216 ≈ 1.21666666666667


Multiply the number by 100/100.

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

1.21666666666667 =

1.21666666666667 × 100/100 =

(1.21666666666667 × 100)/100 =

121.666666666667/100 =

121.666666666667% ≈

121.67%

(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, %
  • 1.216 ≈ 121.67%

» Convert fractions to percentages, online calculator


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

  • 1.216 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 = 1.216


Set up the second equation.

  • Number of decimal places repeating: 1

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


y = 1.216

10 × y = 10 × 1.216

10 × y = 12.16

Get the same number of decimal places as for y:

10 × y = 12.166

Note: 12.166 = 12.16


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 = 12.166 - 1.216 ⇒

(10 - 1) × y = 12.166 - 1.216 ⇒

We now have a new equation:

9 × y = 10.95


Solve for y in the new equation.

9 × y = 10.95 ⇒

y = 10.95/9

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 1.216

According to our calculations:

y = 10.95/9

⇒ 1.216 = 10.95/9


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.

1.216 = (10.95 × 100)/(9 × 100)

1.216 = 1,095/900


3. Reduce (simplify) the fraction above:
1,095/900
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).

1,095 = 3 × 5 × 73

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 (3 × 5 × 73; 22 × 32 × 52) = 3 × 5


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


Divide both the numerator and the denominator by their GCF.

1,095/900 =

(3 × 5 × 73)/(22 × 32 × 52) =

((3 × 5 × 73) ÷ (3 × 5)) / ((22 × 32 × 52) ÷ (3 × 5)) =

73/(22 × 3 × 5) =

73/60


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.

73 ÷ 60 = 1, remainder = 13 ⇒

73 = 1 × 60 + 13 ⇒

73/60 =

(1 × 60 + 13) / 60 =

(1 × 60) / 60 + 13/60 =

1 + 13/60 =

1 13/60


73/60 ~ 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.

73/60 = (73 × 2)/(60 × 2) = 146/120

Example 2. By expanding the fraction by 5.

73/60 = (73 × 5)/(60 × 5) = 365/300

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 73/60

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
1.216 = 73/60

As a mixed number:
1.216 = 1 13/60

As a percentage:
1.216 ≈ 121.67%

As equivalent fractions:
1.216 = 73/60 = 146/120 = 365/300

More operations of this kind

1.217 = ? Convert the mixed repeating (recurring) decimal number 1.217. 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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