Convert the decimal number 0.455. 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 0.455
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
0.455 =
0.455 × 100/100 =
(0.455 × 100)/100 =
45.5/100 =
45.5%
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.455 = 45.5%
2. Write the number as a proper fraction.
0.455 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.455 = 0.455/1
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.
0.455/1 =
(0.455 × 1,000)/(1 × 1,000) =
455/1,000
3. Reduce (simplify) the fraction above: 455/1,000
(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):
455 = 5 × 7 × 13
1,000 = 23 × 53
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (5 × 7 × 13; 23 × 53) = 5
Divide both the numerator and the denominator by their greatest common factor, GCF.
455/1,000 =
(5 × 7 × 13)/(23 × 53) =
((5 × 7 × 13) ÷ 5) / ((23 × 53) ÷ 5) =
(7 × 13)/(23 × 52) =
91/200
91/200: 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 6:
91/200 = (91 × 6)/(200 × 6) = 546/1,200
Example 2. By expanding the fraction by 10:
91/200 = (91 × 10)/(200 × 10) = 910/2,000
Of course, the above fractions are reducing...
... to the initial fraction: 91/200
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.455 = 91/200
As a percentage:
0.455 = 45.5%
As equivalent fractions:
0.455 = 91/200 = 546/1,200 = 910/2,000
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