Convert the decimal number 0.106. 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 0.106
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
0.106 =
0.106 × 100/100 =
(0.106 × 100)/100 =
10.6/100 =
10.6%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.106 = 10.6%
2. Write the number as a proper fraction.
0.106 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.106 = 0.106/1
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.
0.106/1 =
(0.106 × 1,000)/(1 × 1,000) =
106/1,000
3. Reduce (simplify) the fraction above: 106/1,000
(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):
106 = 2 × 53
1,000 = 23 × 53
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2 × 53; 23 × 53) = 2
Divide both the numerator and the denominator by their greatest common factor, GCF.
106/1,000 =
(2 × 53)/(23 × 53) =
((2 × 53) ÷ 2) / ((23 × 53) ÷ 2) =
53/(22 × 53) =
53/500
53/500: 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:
53/500 = (53 × 3)/(500 × 3) = 159/1,500
Example 2. By expanding the fraction by 6:
53/500 = (53 × 6)/(500 × 6) = 318/3,000
Of course, the above fractions are reducing...
... to the initial fraction: 53/500
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.106 = 53/500
As a percentage:
0.106 = 10.6%
As equivalent fractions:
0.106 = 53/500 = 159/1,500 = 318/3,000
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