Convert the pure repeating (recurring) decimal number 0.12129. 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 0.12129
1. Write the pure repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.12129 ≈ 0.12129121291213
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.12129121291213 =
0.12129121291213 × 100/100 =
(0.12129121291213 × 100)/100 =
12.129121291213/100 =
12.129121291213% ≈
12.13%
(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, %
0.12129 ≈ 12.13%
2. Write the pure repeating (recurring) decimal number as a proper fraction.
0.12129 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 = 0.12129
Set up the second equation.
Number of decimal places repeating: 5
Multiply both sides of the first equation by 105 = 100,000
y = 0.12129
100,000 × y = 100,000 × 0.12129
100,000 × y = 12,129.12129
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.
100,000 × y - y = 12,129.12129 - 0.12129 ⇒
(100,000 - 1) × y = 12,129.12129 - 0.12129 ⇒
We now have a new equation:
99,999 × y = 12,129
Solve for y in the new equation.
99,999 × y = 12,129 ⇒
y = 12,129/99,999
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.12129
According to our calculations:
y = 12,129/99,999
⇒ 0.12129 = 12,129/99,999
3. Reduce (simplify) the fraction above: 12,129/99,999
(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):
12,129 = 3 × 13 × 311
99,999 = 32 × 41 × 271
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (3 × 13 × 311; 32 × 41 × 271) = 3
Divide both the numerator and the denominator by their greatest common factor, GCF.
12,129/99,999 =
(3 × 13 × 311)/(32 × 41 × 271) =
((3 × 13 × 311) ÷ 3) / ((32 × 41 × 271) ÷ 3) =
(13 × 311)/(3 × 41 × 271) =
4,043/33,333
4,043/33,333: 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 2:
4,043/33,333 = (4,043 × 2)/(33,333 × 2) = 8,086/66,666
Example 2. By expanding the fraction by 6:
4,043/33,333 = (4,043 × 6)/(33,333 × 6) = 24,258/199,998
Of course, the above fractions are reducing...
... to the initial fraction: 4,043/33,333
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.12129 = 4,043/33,333
As a percentage:
0.12129 ≈ 12.13%
As equivalent fractions:
0.12129 = 4,043/33,333 = 8,086/66,666 = 24,258/199,998
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