Convert the decimal number 0.108. 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 0.108
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
0.108 =
0.108 × 100/100 =
(0.108 × 100)/100 =
10.8/100 =
10.8%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.108 = 10.8%
2. Write the number as a proper fraction.
0.108 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.108 = 0.108/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 1,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.108/1 =
(0.108 × 1,000)/(1 × 1,000) =
108/1,000
3. Reduce (simplify) the fraction above: 108/1,000
(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):
108 = 22 × 33
1,000 = 23 × 53
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (22 × 33; 23 × 53) = 22
Divide both the numerator and the denominator by their greatest common factor, GCF.
108/1,000 =
(22 × 33)/(23 × 53) =
((22 × 33) ÷ 22) / ((23 × 53) ÷ 22) =
33/(2 × 53) =
27/250
27/250: 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:
27/250 = (27 × 2)/(250 × 2) = 54/500
Example 2. By expanding the fraction by 3:
27/250 = (27 × 3)/(250 × 3) = 81/750
Of course, the above fractions are reducing...
... to the initial fraction: 27/250
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.108 = 27/250
As a percentage:
0.108 = 10.8%
As equivalent fractions:
0.108 = 27/250 = 54/500 = 81/750
More operations of this kind
Decimal numbers to fractions and percentages, calculator