Convert the mixed repeating (recurring) decimal number 3.02. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator
Convert 3.02 into equivalent fractions and write it as a percentage value
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14).
Multiply the number by 100/100.
- The value of the number does not change when multiplying by 100/100.
- Note: 100/100 = 1
3.02222222222222 =
3.02222222222222 × 100/100 =
(3.02222222222222 × 100)/100 =
302.222222222222/100 =
302.222222222222% ≈
302.22%
(rounded off to max. 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, %
- 3.02 ≈ 302.22%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
3.02 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 = 3.02
Set up the second equation.
- Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 3.02
10 × y = 10 × 3.02
10 × y = 30.2
Get the same number of decimal places as for y:
10 × y = 30.22
Note: 30.22 = 30.2
Subtract the first equation from the second one.
- Having the same number of decimal places ...
- The repeating pattern drops off by subtracting the two equations.
10 × y - y = 30.22 - 3.02 ⇒
(10 - 1) × y = 30.22 - 3.02 ⇒
We now have a new equation:
9 × y = 27.2
Solve for y in the new equation.
9 × y = 27.2 ⇒
y = 27.2/9
Let the result written as a fraction.
Now we can write the number as a fraction.
According to our first equation:
y = 3.02
According to our calculations:
y = 27.2/9
⇒ 3.02 = 27.2/9
Get rid of the decimal places in the fraction above.
- Multiply the top and the bottom number by 10.
- 1 followed by as many 0-s as the number of digits after the decimal point.
3.02 = (27.2 × 10)/(9 × 10)
3.02 = 272/90
3. Reduce (simplify) the fraction above:
272/90
to the lowest terms, to its simplest equivalent form, irreducible.
To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.
Factor the numerator and denominator (prime factorization).
272 = 24 × 17
90 = 2 × 32 × 5
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (24 × 17; 2 × 32 × 5) = 2
Divide both the numerator and the denominator by their GCF.
272/90 =
(24 × 17)/(2 × 32 × 5) =
((24 × 17) ÷ 2) / ((2 × 32 × 5) ÷ 2) =
(23 × 17)/(32 × 5) =
136/45
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.
136 ÷ 45 = 3, remainder = 1 ⇒
136 = 3 × 45 + 1 ⇒
136/45 =
(3 × 45 + 1) / 45 =
(3 × 45) / 45 + 1/45 =
3 + 1/45 =
3 1/45
136/45 ~ 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.
136/45 = (136 × 3)/(45 × 3) = 408/135
Example 2. By expanding the fraction by 5.
136/45 = (136 × 5)/(45 × 5) = 680/225
- Of course, the above fractions are reducing...
- ... to the initial fraction: 136/45
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
3.02 = 136/45
As a mixed number:
3.02 = 3 1/45
As a percentage:
3.02 ≈ 302.22%
As equivalent fractions:
3.02 = 136/45 = 408/135 = 680/225
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