Convert the mixed repeating (recurring) decimal number 0.307693. 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 0.307693
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.307693 ≈ 0.30769333333333
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.30769333333333 =
0.30769333333333 × 100/100 =
(0.30769333333333 × 100)/100 =
30.769333333333/100 =
30.769333333333% ≈
30.77%
(rounded off to a maximum of 2 decimal places)
In other words:
Approximate to the desired number of decimal places...
Multiply the number by 100...
... And then add the percent sign, %
0.307693 ≈ 30.77%
2. Write the mixed repeating (recurring) decimal number as a proper fraction.
0.307693 can be written as a proper fraction. The numerator is smaller than the denominator.
Set up the first equation.
Let y equal the decimal number:
y = 0.307693
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 0.307693
10 × y = 10 × 0.307693
10 × y = 3.07693
Get the same number of decimal places as for y:
10 × y = 3.076933
Note: 3.076933 = 3.07693
Subtract the first equation from the second equation.
Having the same number of decimal places ...
The repeating pattern drops off by subtracting the two equations.
10 × y - y = 3.076933 - 0.307693 ⇒
(10 - 1) × y = 3.076933 - 0.307693 ⇒
We now have a new equation:
9 × y = 2.76924
Solve for y in the new equation.
9 × y = 2.76924 ⇒
y = 2.76924/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.307693
According to our calculations:
y = 2.76924/9
⇒ 0.307693 = 2.76924/9
Get rid of the decimal places in the fraction above.
Multiply the top and the bottom number by 100,000.
1 followed by as many 0-s as the number of digits after the decimal point.
0.307693 = (2.76924 × 100,000)/(9 × 100,000)
0.307693 = 276,924/900,000
3. Reduce (simplify) the fraction above: 276,924/900,000
(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):
276,924 = 22 × 3 × 47 × 491
900,000 = 25 × 32 × 55
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (22 × 3 × 47 × 491; 25 × 32 × 55) = 22 × 3
Divide both the numerator and the denominator by their greatest common factor, GCF.
276,924/900,000 =
(22 × 3 × 47 × 491)/(25 × 32 × 55) =
((22 × 3 × 47 × 491) ÷ (22 × 3)) / ((25 × 32 × 55) ÷ (22 × 3)) =
(47 × 491)/(23 × 3 × 55) =
23,077/75,000
23,077/75,000: 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 3:
23,077/75,000 = (23,077 × 3)/(75,000 × 3) = 69,231/225,000
Example 2. By expanding the fraction by 5:
23,077/75,000 = (23,077 × 5)/(75,000 × 5) = 115,385/375,000
Of course, the above fractions are reducing...
... to the initial fraction: 23,077/75,000
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.307693 = 23,077/75,000
As a percentage:
0.307693 ≈ 30.77%
As equivalent fractions:
0.307693 = 23,077/75,000 = 69,231/225,000 = 115,385/375,000
More operations of this kind
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