Menu Convert the mixed repeating (recurring) decimal number 2.275342 . 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 Write the mixed repeating (recurring) decimal 2.275342 . As a reduced (simplified) positive improper fraction. As a mixed number. As a percentage. As equivalent fractions. More operations of this kind: 2.275343 = ?
1. Write the mixed repeating (recurring) decimal number as a percentage.
Approximate to the desired number of decimal places (14): 2.275342 ≈ 2.27534234234234 Multiply the number by 100 /100 . The value of the number does not change when multiplying by 100 /100 . Note: 100 /100 = 1
2.27534234234234 = 2.27534234234234 × 100 /100 = (2.27534234234234 × 100) /100 = 227.534234234234 /100 = 227.534234234234% ≈ 227.53% (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, % 2.275342 ≈ 227.53%
2. Write the mixed repeating (recurring) decimal number as an improper fraction. 2.275342 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 = 2.275342 Set up the second equation. Number of decimal places repeating: 3 Multiply both sides of the first equation by 103 = 1,000
y = 2.275342 1,000 × y = 1,000 × 2.275342 1,000 × y = 2,275.342 Get the same number of decimal places as for y: 1,000 × y = 2,275.342342 Note: 2,275.342342 = 2,275.342 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.
1,000 × y - y = 2,275.342342 - 2.275342 => (1,000 - 1) × y = 2,275.342342 - 2.275342 => We now have a new equation: 999 × y = 2,273.067
Solve for y in the new equation.
999 × y = 2,273.067 => y = 2,273.067 /999 Let the result written down as a fraction. Write the number as a fraction.
According to our first equation: y = 2.275342 According to our calculations: y = 2,273.067 /999 => 2.275342 = 2,273.067 /999 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 0s as the number of digits after the decimal point) 2.275342 = (2,273.067 × 1,000) /(999 × 1,000) 2.275342 = 2,273,067 /999,000
3. Reduce (simplify) the fraction above: 2,273,067 /999,000 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 ): 2,273,067 = 32 × 23 × 79 × 139 999,000 = 23 × 33 × 53 × 37 Calculate the greatest (highest) common factor (divisor), GCF.
Multiply all the common prime factors by the lowest exponents. GCF (32 × 23 × 79 × 139; 23 × 33 × 53 × 37) = 32 Divide both the numerator and the denominator by their greatest common factor, GCF.
2,273,067 /999,000 = (32 × 23 × 79 × 139) /(23 × 33 × 53 × 37) = ((32 × 23 × 79 × 139) ÷ 32 ) / ((23 × 33 × 53 × 37) ÷ 32 ) = (23 × 79 × 139) /(23 × 3 × 53 × 37) = 252,563 /111,000
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.
252,563 ÷ 111,000 = 2, remainder = 30,563 => 252,563 = 2 × 111,000 + 30,563 => 252,563 /111,000 (2 × 111,000 + 30,563) / 111,000 = (2 × 111,000) / 111,000 + 30,563 /111,000 = 2 + 30,563 /111,000 = 2 30,563 /111,000
252,563 /111,000
The above fraction cannot be reduced. That is, it has the smallest numerator and denominator possible. 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: 252,563 /111,000 = (252,563 × 4) /(111,000 × 4) = 1,010,252 /444,000 Example 2. By expanding the fraction by 5: 252,563 /111,000 = (252,563 × 5) /(111,000 × 5) = 1,262,815 /555,000
Of course, the above fractions are reducing... ... to the initial fraction: 252,563 /111,000
:: Final answer :: As a reduced (simplified) positive improper fraction: 342 = 252,563 /111,000 As a mixed number: 342 = 2 30,563 /111,000 As a percentage: 342 ≈ 227.53% As equivalent fractions: 342 = 252,563 /111,000 1,010,252 /444,000 1,262,815 /555,000 More operations of this kind: Decimal numbers to fractions and percentages, calculator
The latest integers, terminating and repeating (recurring) decimal numbers converted to fractions and turned into percentages 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. More on ordinary (common) math fractions theory: