Convert the decimal number 0.1168. 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 0.1168
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
0.1168 =
0.1168 × 100/100 =
(0.1168 × 100)/100 =
11.68/100 =
11.68%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.1168 = 11.68%
2. Write the number as a proper fraction.
0.1168 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.1168 = 0.1168/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 10,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.1168/1 =
(0.1168 × 10,000)/(1 × 10,000) =
1,168/10,000
3. Reduce (simplify) the fraction above: 1,168/10,000
(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):
1,168 = 24 × 73
10,000 = 24 × 54
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (24 × 73; 24 × 54) = 24
Divide both the numerator and the denominator by their greatest common factor, GCF.
1,168/10,000 =
(24 × 73)/(24 × 54) =
((24 × 73) ÷ 24) / ((24 × 54) ÷ 24) =
73/54 =
73/625
73/625: 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:
73/625 = (73 × 5)/(625 × 5) = 365/3,125
Example 2. By expanding the fraction by 6:
73/625 = (73 × 6)/(625 × 6) = 438/3,750
Of course, the above fractions are reducing...
... to the initial fraction: 73/625
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.1168 = 73/625
As a percentage:
0.1168 = 11.68%
As equivalent fractions:
0.1168 = 73/625 = 365/3,125 = 438/3,750
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