Convert the mixed repeating (recurring) decimal number 0.729. 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 0.729
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
0.729 ≈ 0.72929292929293
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
0.72929292929293 =
0.72929292929293 × 100/100 =
(0.72929292929293 × 100)/100 =
72.929292929293/100 =
72.929292929293% ≈
72.93%
(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, %
0.729 ≈ 72.93%
2. Write the mixed repeating (recurring) decimal number as a proper fraction.
0.729 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 = 0.729
Set up the second equation.
Number of decimal places repeating: 2
Multiply both sides of the first equation by 102 = 100
y = 0.729
100 × y = 100 × 0.729
100 × y = 72.929
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.
100 × y - y = 72.929 - 0.729 ⇒
(100 - 1) × y = 72.929 - 0.729 ⇒
We now have a new equation:
99 × y = 72
Solve for y in the new equation.
99 × y = 72 ⇒
y = 72/99
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 0.729
According to our calculations:
y = 72/99
⇒ 0.729 = 72/99
3. Reduce (simplify) the fraction above: 72/99
(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):
72 = 23 × 32
99 = 32 × 11
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (23 × 32; 32 × 11) = 32
Divide both the numerator and the denominator by their greatest common factor, GCF.
72/99 =
(23 × 32)/(32 × 11) =
((23 × 32) ÷ 32) / ((32 × 11) ÷ 32) =
23/11 =
8/11
8/11: 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:
8/11 = (8 × 3)/(11 × 3) = 24/33
Example 2. By expanding the fraction by 4:
8/11 = (8 × 4)/(11 × 4) = 32/44
Of course, the above fractions are reducing...
... to the initial fraction: 8/11
:: Final answer ::
Written in 3 different ways
As a reduced (simplified) positive proper fraction:
0.729 = 8/11
As a percentage:
0.729 ≈ 72.93%
As equivalent fractions:
0.729 = 8/11 = 24/33 = 32/44
More operations of this kind
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