Convert the mixed repeating (recurring) decimal number 3.1419. 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 3.1419
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places:
3.1419 ≈ 3.142
Multiply the number by 100/100.
The value of the number does not change when multiplying by 100/100.
Note: 100/100 = 1
3.142 =
3.142 × 100/100 =
(3.142 × 100)/100 =
314.2/100 =
314.2%
In other words:
Approximate to the desired number of decimal places...
Multiply the number by 100...
... And then add the percent sign, %
3.1419 ≈ 314.2%
2. Write the mixed repeating (recurring) decimal number as an improper fraction.
3.1419 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 = 3.1419
Set up the second equation.
Number of decimal places repeating: 1
Multiply both sides of the first equation by 101 = 10
y = 3.1419
10 × y = 10 × 3.1419
10 × y = 31.419
Get the same number of decimal places as for y:
10 × y = 31.4199
Note: 31.4199 = 31.419
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 = 31.4199 - 3.1419 =>
(10 - 1) × y = 31.4199 - 3.1419 =>
We now have a new equation:
9 × y = 28.278
Solve for y in the new equation.
9 × y = 28.278 =>
y = 28.278/9
Let the result written as a fraction.
Write the number as a fraction.
According to our first equation:
y = 3.1419
According to our calculations:
y = 28.278/9
=> 3.1419 = 28.278/9
Get rid of the decimal places in the fraction above.
Multiply the top and the bottom number by 1,000.
1 followed by as many 0-s as the number of digits after the decimal point.
3.1419 = (28.278 × 1,000)/(9 × 1,000)
3.1419 = 28,278/9,000
3. Reduce (simplify) the fraction above: 28,278/9,000
(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):
28,278 = 2 × 32 × 1,571
9,000 = 23 × 32 × 53
Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents.
GCF (2 × 32 × 1,571; 23 × 32 × 53) = 2 × 32
Divide both the numerator and the denominator by their greatest common factor, GCF.
28,278/9,000 =
(2 × 32 × 1,571)/(23 × 32 × 53) =
((2 × 32 × 1,571) ÷ (2 × 32)) / ((23 × 32 × 53) ÷ (2 × 32)) =
1,571/(22 × 53) =
1,571/500
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.
1,571 ÷ 500 = 3, remainder = 71 =>
1,571 = 3 × 500 + 71 =>
1,571/500 =
(3 × 500 + 71) / 500 =
(3 × 500) / 500 + 71/500 =
3 + 71/500 =
3 71/500
1,571/500: 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 2:
1,571/500 = (1,571 × 2)/(500 × 2) = 3,142/1,000
Example 2. By expanding the fraction by 4:
1,571/500 = (1,571 × 4)/(500 × 4) = 6,284/2,000
Of course, the above fractions are reducing...
... to the initial fraction: 1,571/500
:: Final answer ::
Written in 4 different ways
As a reduced (simplified) positive improper fraction:
3.1419 = 1,571/500
As a mixed number:
3.1419 = 3 71/500
As a percentage:
3.1419 = 314.2%
As equivalent fractions:
3.1419 = 1,571/500 = 3,142/1,000 = 6,284/2,000
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Learn how to turn a decimal number into a fraction and a percentage. Steps.
1. How to write the number as a percentage:
- Multiply the number by 100. Then add the percent sign, %.
2. How to write the number as a fraction:
- Write down the number divided by 1, as a fraction.
- Turn the top number into a whole number: multiply both the top and the bottom by the same number.
- Reduce (simplify) the above fraction 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.
- If the fraction is an improper one, rewrite it as a mixed number (mixed fraction).
- Calculate equivalent fractions. By expanding it we can build up equivalent fractions: multiply the numerator & the denominator by the same number.
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