Convert the mixed repeating (recurring) decimal number 16.839. 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 16.839

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

Approximate to the desired number of decimal places:


16.83916.84


Multiply the number by 100/100.

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

Note: 100/100 = 1

16.84 =


16.84 × 100/100 =


(16.84 × 100)/100 =


1,684/100 =


1,684%


In other words:


Approximate to the desired number of decimal places...


Multiply the number by 100...


... And then add the percent sign, %


16.8391,684%


Convert fractions to percentages, online calculator


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

16.839 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 = 16.839


Set up the second equation.

Number of decimal places repeating: 1

Multiply both sides of the first equation by 101 = 10

y = 16.839


10 × y = 10 × 16.839


10 × y = 168.39


Get the same number of decimal places as for y:


10 × y = 168.399


Note: 168.399 = 168.39


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 = 168.399 - 16.839 =>


(10 - 1) × y = 168.399 - 16.839 =>


We now have a new equation:


9 × y = 151.56


Solve for y in the new equation.

9 × y = 151.56 =>


y = 151.56/9

Let the result written down as a fraction.


Write the number as a fraction.

According to our first equation:


y = 16.839


According to our calculations:


y = 151.56/9


=> 16.839 = 151.56/9


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)


16.839 = (151.56 × 100)/(9 × 100)


16.839 = 15,156/900


3. Reduce (simplify) the fraction above: 15,156/900
(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):


15,156 = 22 × 32 × 421


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.


GCF (22 × 32 × 421; 22 × 32 × 52) = 22 × 32

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


Divide both the numerator and the denominator by their greatest common factor, GCF.

15,156/900 =


(22 × 32 × 421)/(22 × 32 × 52) =


((22 × 32 × 421) ÷ (22 × 32)) / ((22 × 32 × 52) ÷ (22 × 32)) =


421/52 =


421/25


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.


421 ÷ 25 = 16, remainder = 21 =>


421 = 16 × 25 + 21 =>


421/25 =


(16 × 25 + 21) / 25 =


(16 × 25) / 25 + 21/25 =


16 + 21/25 =


16 21/25


421/25: 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 4:

421/25 = (421 × 4)/(25 × 4) = 1,684/100

Example 2. By expanding the fraction by 6:

421/25 = (421 × 6)/(25 × 6) = 2,526/150

Of course, the above fractions are reducing...


... to the initial fraction: 421/25


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
16.839 = 421/25

As a mixed number:
16.839 = 16 21/25

As a percentage:
16.839 = 1,684%

As equivalent fractions:
16.839 = 421/25 = 1,684/100 = 2,526/150

More operations of this kind:

16.84 = ?

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