Convert the decimal number 0.22222229. 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 0.22222229
1. Write the number as a percentage.
Multiply the number by 100/100
Note: 100/100 = 1
The value of the number does not change when multiplying by 100/100
0.22222229 =
0.22222229 × 100/100 =
(0.22222229 × 100)/100 =
22.222229/100 =
22.222229% ≈
22.22%
(rounded off to a maximum of 2 decimal places)
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.22222229 ≈ 22.22%
2. Write the number as a proper fraction.
0.22222229 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.22222229 = 0.22222229/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 100,000,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.22222229/1 =
(0.22222229 × 100,000,000)/(1 × 100,000,000) =
22,222,229/100,000,000
3. Reduce (simplify) the fraction above: 22,222,229/100,000,000
(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):
22,222,229 = 19 × 1,169,591
100,000,000 = 28 × 58
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
But, the numerator and the denominator have no common factors.
GCF (19 × 1,169,591; 28 × 58) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
22,222,229/100,000,000: 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:
22,222,229/100,000,000 = (22,222,229 × 5)/(100,000,000 × 5) = 111,111,145/500,000,000
Example 2. By expanding the fraction by 6:
22,222,229/100,000,000 = (22,222,229 × 6)/(100,000,000 × 6) = 133,333,374/600,000,000
Of course, the above fractions are reducing...
... to the initial fraction: 22,222,229/100,000,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.22222229 = 22,222,229/100,000,000
As a percentage:
0.22222229 ≈ 22.22%
As equivalent fractions:
0.22222229 = 22,222,229/100,000,000 = 111,111,145/500,000,000 = 133,333,374/600,000,000
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