Convert the pure repeating (recurring) decimal number 0.0328200603. 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 0.0328200603
1. Write the pure repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.0328200603 ≈ 0.03282006030328
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.03282006030328 =
0.03282006030328 × 100/100 =
(0.03282006030328 × 100)/100 =
3.282006030328/100 =
3.282006030328% ≈
3.28%
(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, %
0.0328200603 ≈ 3.28%
2. Write the pure repeating (recurring) decimal number as a proper fraction.
0.0328200603 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 = 0.0328200603
Set up the second equation.
Number of decimal places repeating: 10
Multiply both sides of the first equation by 1010 = 10,000,000,000
y = 0.0328200603
10,000,000,000 × y = 10,000,000,000 × 0.0328200603
10,000,000,000 × y = 328,200,603.0328200603
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.
10,000,000,000 × y - y = 328,200,603.0328200603 - 0.0328200603 ⇒
(10,000,000,000 - 1) × y = 328,200,603.0328200603 - 0.0328200603 ⇒
We now have a new equation:
9,999,999,999 × y = 328,200,603
Solve for y in the new equation.
9,999,999,999 × y = 328,200,603 ⇒
y = 328,200,603/9,999,999,999
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.0328200603
According to our calculations:
y = 328,200,603/9,999,999,999
⇒ 0.0328200603 = 328,200,603/9,999,999,999
3. Reduce (simplify) the fraction above: 328,200,603/9,999,999,999
(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):
328,200,603 = 3 × 181 × 491 × 1,231
9,999,999,999 = 32 × 11 × 41 × 271 × 9,091
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (3 × 181 × 491 × 1,231; 32 × 11 × 41 × 271 × 9,091) = 3
Divide both the numerator and the denominator by their greatest common factor, GCF.
328,200,603/9,999,999,999 =
(3 × 181 × 491 × 1,231)/(32 × 11 × 41 × 271 × 9,091) =
((3 × 181 × 491 × 1,231) ÷ 3) / ((32 × 11 × 41 × 271 × 9,091) ÷ 3) =
(181 × 491 × 1,231)/(3 × 11 × 41 × 271 × 9,091) =
109,400,201/3,333,333,333
109,400,201/3,333,333,333: 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:
109,400,201/3,333,333,333 = (109,400,201 × 2)/(3,333,333,333 × 2) = 218,800,402/6,666,666,666
Example 2. By expanding the fraction by 6:
109,400,201/3,333,333,333 = (109,400,201 × 6)/(3,333,333,333 × 6) = 656,401,206/19,999,999,998
Of course, the above fractions are reducing...
... to the initial fraction: 109,400,201/3,333,333,333
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.0328200603 = 109,400,201/3,333,333,333
As a percentage:
0.0328200603 ≈ 3.28%
As equivalent fractions:
0.0328200603 = 109,400,201/3,333,333,333 = 218,800,402/6,666,666,666 = 656,401,206/19,999,999,998
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