Convert the decimal number 0.027778. 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 0.027778
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
0.027778 =
0.027778 × 100/100 =
(0.027778 × 100)/100 =
2.7778/100 =
2.7778% ≈
2.78%
(rounded off to a maximum of 2 decimal places)
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.027778 ≈ 2.78%
2. Write the number as a proper fraction.
0.027778 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.027778 = 0.027778/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 1,000,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.027778/1 =
(0.027778 × 1,000,000)/(1 × 1,000,000) =
27,778/1,000,000
3. Reduce (simplify) the fraction above: 27,778/1,000,000
(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):
27,778 = 2 × 17 × 19 × 43
1,000,000 = 26 × 56
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2 × 17 × 19 × 43; 26 × 56) = 2
Divide both the numerator and the denominator by their greatest common factor, GCF.
27,778/1,000,000 =
(2 × 17 × 19 × 43)/(26 × 56) =
((2 × 17 × 19 × 43) ÷ 2) / ((26 × 56) ÷ 2) =
(17 × 19 × 43)/(25 × 56) =
13,889/500,000
13,889/500,000: 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 3:
13,889/500,000 = (13,889 × 3)/(500,000 × 3) = 41,667/1,500,000
Example 2. By expanding the fraction by 7:
13,889/500,000 = (13,889 × 7)/(500,000 × 7) = 97,223/3,500,000
Of course, the above fractions are reducing...
... to the initial fraction: 13,889/500,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.027778 = 13,889/500,000
As a percentage:
0.027778 ≈ 2.78%
As equivalent fractions:
0.027778 = 13,889/500,000 = 41,667/1,500,000 = 97,223/3,500,000
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