Convert the mixed repeating (recurring) decimal number 2.458. 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 2.458

1. Write the mixed repeating (recurring) decimal number as a percentage.

Approximate to the desired number of decimal places (14):


2.4582.45888888888889


Multiply the number by 100/100.

The value of the number does not change when multiplying by 100/100.

Note: 100/100 = 1

2.45888888888889 =


2.45888888888889 × 100/100 =


(2.45888888888889 × 100)/100 =


245.888888888889/100 =


245.888888888889% ≈


245.89%


(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, %


2.458245.89%


Convert fractions to percentages, online calculator


2. Write the mixed repeating (recurring) decimal number as an improper fraction.

2.458 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 = 2.458


Set up the second equation.

Number of decimal places repeating: 1

Multiply both sides of the first equation by 101 = 10

y = 2.458


10 × y = 10 × 2.458


10 × y = 24.58


Get the same number of decimal places as for y:


10 × y = 24.588


Note: 24.588 = 24.58


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 = 24.588 - 2.458 =>


(10 - 1) × y = 24.588 - 2.458 =>


We now have a new equation:


9 × y = 22.13


Solve for y in the new equation.

9 × y = 22.13 =>


y = 22.13/9

Let the result written down as a fraction.


Write the number as a fraction.

According to our first equation:


y = 2.458


According to our calculations:


y = 22.13/9


=> 2.458 = 22.13/9


Get rid of the decimal places in the fraction above.

Multiply the top and the bottom number by 100:


(1 followed by as many 0s as the number of digits after the decimal point)


2.458 = (22.13 × 100)/(9 × 100)


2.458 = 2,213/900


3. Reduce (simplify) the fraction above: 2,213/900
(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):


2,213 is a prime number, it cannot be factored into other prime factors


900 = 22 × 32 × 52

Prime factorization: break numbers down to prime factors, online calculator


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 (2,213; 22 × 32 × 52) = 1

Calculate the greatest (highest) common factor (divisor), GCF, online calculator



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.


2,213 ÷ 900 = 2, remainder = 413 =>


2,213 = 2 × 900 + 413 =>


2,213/900 =


(2 × 900 + 413) / 900 =


(2 × 900) / 900 + 413/900 =


2 + 413/900 =


2 413/900


2,213/900: Equivalent fractions.

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 2:

2,213/900 = (2,213 × 2)/(900 × 2) = 4,426/1,800

Example 2. By expanding the fraction by 4:

2,213/900 = (2,213 × 4)/(900 × 4) = 8,852/3,600

Of course, the above fractions are reducing...


... to the initial fraction: 2,213/900


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
2.458 = 2,213/900

As a mixed number:
2.458 = 2 413/900

As a percentage:
2.458 ≈ 245.89%

As equivalent fractions:
2.458 = 2,213/900 = 4,426/1,800 = 8,852/3,600

More operations of this kind:

2.459 = ?

Decimal numbers to fractions and percentages, calculator

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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:

2. How to write the number as a fraction:

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers