Convert the mixed repeating (recurring) decimal number 7.28476. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding
Convert 7.28476
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14):
7.28476 ≈ 7.28476767676768
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
7.28476767676768 =
7.28476767676768 × 100/100 =
(7.28476767676768 × 100)/100 =
728.476767676768/100 =
728.476767676768% ≈
728.48%
(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, %
7.28476 ≈ 728.48%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
7.28476 can be written as an improper fraction. The numerator is larger than or equal to the denominator.
Set up the first equation.
Let y equal the decimal number:
y = 7.28476
Set up the second equation.
Number of decimal places repeating: 2
Multiply both sides of the first equation by 102 = 100
y = 7.28476
100 × y = 100 × 7.28476
100 × y = 728.476
Get the same number of decimal places as for y:
100 × y = 728.47676
Note: 728.47676 = 728.476
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 = 728.47676 - 7.28476 ⇒
(100 - 1) × y = 728.47676 - 7.28476 ⇒
We now have a new equation:
99 × y = 721
Solve for y in the new equation.
99 × y = 721 ⇒
y = 721/99
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 7.28476
According to our calculations:
y = 721/99
⇒ 7.28476 = 721/99
3. Reduce (simplify) the fraction above: 721/99
(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):
721 = 7 × 103
99 = 32 × 11
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 × 103; 32 × 11) = 1
The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1). So, the fraction cannot be reduced (simplified): irreducible fraction.
4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):
A mixed number = an integer number and a proper fraction, of the same sign.
Example 1: 2 1/5; Example 2: - 1 3/7.
A proper fraction = the numerator is smaller than the denominator.
721 ÷ 99 = 7, remainder = 28 ⇒
721 = 7 × 99 + 28 ⇒
721/99 =
(7 × 99 + 28) / 99 =
(7 × 99) / 99 + 28/99 =
7 + 28/99 =
7 28/99
721/99: 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:
721/99 = (721 × 4)/(99 × 4) = 2,884/396
Example 2. By expanding the fraction by 8:
721/99 = (721 × 8)/(99 × 8) = 5,768/792
Of course, the above fractions are reducing...
... to the initial fraction: 721/99
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
7.28476 = 721/99
As a mixed number:
7.28476 = 7 28/99
As a percentage:
7.28476 ≈ 728.48%
As equivalent fractions:
7.28476 = 721/99 = 2,884/396 = 5,768/792
More operations of this kind
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