Convert the mixed repeating (recurring) decimal number 3.142. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Equivalent fractions calculator
Convert 3.142 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):
3.142 ≈ 3.14222222222222
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
3.14222222222222 =
3.14222222222222 × 100/100 =
(3.14222222222222 × 100)/100 =
314.222222222222/100 =
314.222222222222% ≈
314.22%
(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, %
3.142 ≈ 314.22%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
3.142 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 = 3.142
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 3.142
10 × y = 10 × 3.142
10 × y = 31.42
Get the same number of decimal places as for y:
10 × y = 31.422
Note: 31.422 = 31.42
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 = 31.422 - 3.142 ⇒
(10 - 1) × y = 31.422 - 3.142 ⇒
We now have a new equation:
9 × y = 28.28
Solve for y in the new equation.
9 × y = 28.28 ⇒
y = 28.28/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 3.142
According to our calculations:
y = 28.28/9
⇒ 3.142 = 28.28/9
Get rid of the decimal places in the fraction above.
Multiply the top and the bottom number by 100.
1 followed by as many 0-s as the number of digits after the decimal point.
3.142 = (28.28 × 100)/(9 × 100)
3.142 = 2,828/900
3. Reduce (simplify) the fraction above: 2,828/900
(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):
2,828 = 22 × 7 × 101
900 = 22 × 32 × 52
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (22 × 7 × 101; 22 × 32 × 52) = 22
Divide both the numerator and the denominator by their greatest common factor, GCF.
2,828/900 =
(22 × 7 × 101)/(22 × 32 × 52) =
((22 × 7 × 101) ÷ 22) / ((22 × 32 × 52) ÷ 22) =
(7 × 101)/(32 × 52) =
707/225
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.
707 ÷ 225 = 3, remainder = 32 ⇒
707 = 3 × 225 + 32 ⇒
707/225 =
(3 × 225 + 32) / 225 =
(3 × 225) / 225 + 32/225 =
3 + 32/225 =
3 32/225
707/225: 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:
707/225 = (707 × 5)/(225 × 5) = 3,535/1,125
Example 2. By expanding the fraction by 9:
707/225 = (707 × 9)/(225 × 9) = 6,363/2,025
Of course, the above fractions are reducing...
... to the initial fraction: 707/225
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
3.142 = 707/225
As a mixed number:
3.142 = 3 32/225
As a percentage:
3.142 ≈ 314.22%
As equivalent fractions:
3.142 = 707/225 = 3,535/1,125 = 6,363/2,025
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