Convert the decimal number 0.000777. 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 0.000777
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
0.000777 =
0.000777 × 100/100 =
(0.000777 × 100)/100 =
0.0777/100 =
0.0777% ≈
0.08%
(rounded off to a maximum of 2 decimal places)
In other words:
Multiply the number by 100...
... And then add the percent sign, %
0.000777 ≈ 0.08%
2. Write the number as a proper fraction.
0.000777 can be written as a proper fraction.
The numerator is smaller than the denominator.
Write down the number divided by 1, as a fraction:
0.000777 = 0.000777/1
Turn the top number into a whole number.
Multiply both the top and the bottom by the same number.
This number is: 1,000,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.000777/1 =
(0.000777 × 1,000,000)/(1 × 1,000,000) =
777/1,000,000
3. Reduce (simplify) the fraction above: 777/1,000,000
(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):
777 = 3 × 7 × 37
1,000,000 = 26 × 56
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 × 7 × 37; 26 × 56) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
777/1,000,000: 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 5:
777/1,000,000 = (777 × 5)/(1,000,000 × 5) = 3,885/5,000,000
Example 2. By expanding the fraction by 8:
777/1,000,000 = (777 × 8)/(1,000,000 × 8) = 6,216/8,000,000
Of course, the above fractions are reducing...
... to the initial fraction: 777/1,000,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.000777 = 777/1,000,000
As a percentage:
0.000777 ≈ 0.08%
As equivalent fractions:
0.000777 = 777/1,000,000 = 3,885/5,000,000 = 6,216/8,000,000
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