Convert the pure repeating (recurring) decimal number 0.1218. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding
Convert 0.1218
1. Write the pure repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.1218 ≈ 0.12181218121812
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.12181218121812 =
0.12181218121812 × 100/100 =
(0.12181218121812 × 100)/100 =
12.181218121812/100 =
12.181218121812% ≈
12.18%
(rounded off to a maximum of 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, %
0.1218 ≈ 12.18%
2. Write the pure repeating (recurring) decimal number as a proper fraction.
0.1218 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 = 0.1218
Set up the second equation.
Number of decimal places repeating: 4
Multiply both sides of the first equation by 104 = 10,000
y = 0.1218
10,000 × y = 10,000 × 0.1218
10,000 × y = 1,218.1218
Subtract the first equation from the second equation.
Having the same number of decimal places ...
The repeating pattern drops off by subtracting the two equations.
10,000 × y - y = 1,218.1218 - 0.1218 ⇒
(10,000 - 1) × y = 1,218.1218 - 0.1218 ⇒
We now have a new equation:
9,999 × y = 1,218
Solve for y in the new equation.
9,999 × y = 1,218 ⇒
y = 1,218/9,999
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.1218
According to our calculations:
y = 1,218/9,999
⇒ 0.1218 = 1,218/9,999
3. Reduce (simplify) the fraction above: 1,218/9,999
(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).
In exponential notation (an):
1,218 = 2 × 3 × 7 × 29
9,999 = 32 × 11 × 101
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2 × 3 × 7 × 29; 32 × 11 × 101) = 3
Divide both the numerator and the denominator by their greatest common factor, GCF.
1,218/9,999 =
(2 × 3 × 7 × 29)/(32 × 11 × 101) =
((2 × 3 × 7 × 29) ÷ 3) / ((32 × 11 × 101) ÷ 3) =
(2 × 7 × 29)/(3 × 11 × 101) =
406/3,333
406/3,333: 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 5:
406/3,333 = (406 × 5)/(3,333 × 5) = 2,030/16,665
Example 2. By expanding the fraction by 7:
406/3,333 = (406 × 7)/(3,333 × 7) = 2,842/23,331
Of course, the above fractions are reducing...
... to the initial fraction: 406/3,333
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.1218 = 406/3,333
As a percentage:
0.1218 ≈ 12.18%
As equivalent fractions:
0.1218 = 406/3,333 = 2,030/16,665 = 2,842/23,331
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