Convert the decimal number 0.8128015847. 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 0.8128015847
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
0.8128015847 =
0.8128015847 × 100/100 =
(0.8128015847 × 100)/100 =
81.28015847/100 =
81.28015847% ≈
81.28%
(rounded off to a maximum of 2 decimal places)
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.8128015847 ≈ 81.28%
2. Write the number as a proper fraction.
0.8128015847 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.8128015847 = 0.8128015847/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 10,000,000,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.8128015847/1 =
(0.8128015847 × 10,000,000,000)/(1 × 10,000,000,000) =
8,128,015,847/10,000,000,000
3. Reduce (simplify) the fraction above: 8,128,015,847/10,000,000,000
(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):
8,128,015,847 = 7 × 8,039 × 144,439
10,000,000,000 = 210 × 510
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 (7 × 8,039 × 144,439; 210 × 510) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
8,128,015,847/10,000,000,000: 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 4:
8,128,015,847/10,000,000,000 = (8,128,015,847 × 4)/(10,000,000,000 × 4) = 32,512,063,388/40,000,000,000
Example 2. By expanding the fraction by 7:
8,128,015,847/10,000,000,000 = (8,128,015,847 × 7)/(10,000,000,000 × 7) = 56,896,110,929/70,000,000,000
Of course, the above fractions are reducing...
... to the initial fraction: 8,128,015,847/10,000,000,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.8128015847 = 8,128,015,847/10,000,000,000
As a percentage:
0.8128015847 ≈ 81.28%
As equivalent fractions:
0.8128015847 = 8,128,015,847/10,000,000,000 = 32,512,063,388/40,000,000,000 = 56,896,110,929/70,000,000,000
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