Convert the decimal number 0.1167. 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 0.1167
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
0.1167 =
0.1167 × 100/100 =
(0.1167 × 100)/100 =
11.67/100 =
11.67%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.1167 = 11.67%
2. Write the number as a proper fraction.
0.1167 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.1167 = 0.1167/1
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.
0.1167/1 =
(0.1167 × 10,000)/(1 × 10,000) =
1,167/10,000
3. Reduce (simplify) the fraction above: 1,167/10,000
(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):
1,167 = 3 × 389
10,000 = 24 × 54
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 (3 × 389; 24 × 54) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
1,167/10,000: 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 2:
1,167/10,000 = (1,167 × 2)/(10,000 × 2) = 2,334/20,000
Example 2. By expanding the fraction by 4:
1,167/10,000 = (1,167 × 4)/(10,000 × 4) = 4,668/40,000
Of course, the above fractions are reducing...
... to the initial fraction: 1,167/10,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.1167 = 1,167/10,000
As a percentage:
0.1167 = 11.67%
As equivalent fractions:
0.1167 = 1,167/10,000 = 2,334/20,000 = 4,668/40,000
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