Convert the decimal number - 6.89. 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 - 6.89

1. Write the number as a percentage.

Note: 100/100 = 1

- 6.89 =


- 6.89 × 100/100 =


- (6.89 × 100)/100 =


- 689/100 =


- 689%


In other words:


Multiply the number by 100...


... And then add the percent sign, %


- 6.89 = - 689%


Convert fractions to percentages, online calculator


2. Write the number as an improper fraction.

- 6.89 can be written as an improper fraction.

(The numerator is larger than or equal to the denominator).

Write down the number divided by 1, as a fraction:

- 6.89 = - 6.89/1

Turn the top number into a whole number.

Multiply both the top and the bottom by the same number.


This number is: 100.


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


- 6.89/1 =


- (6.89 × 100)/(1 × 100) =


- 689/100


3. Reduce (simplify) the fraction above: - 689/100
(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):


689 = 13 × 53


100 = 22 × 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 (13 × 53; 22 × 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.


- 689 ÷ 100 = - 6, remainder = - 89 =>


- 689 = - 6 × 100 - 89 =>


- 689/100 =


(- 6 × 100 - 89) / 100 =


(- 6 × 100) / 100 - 89/100 =


- 6 - 89/100 =


- 6 89/100


- 689/100: 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:

- 689/100 = - (689 × 4)/(100 × 4) = - 2,756/400

Example 2. By expanding the fraction by 5:

- 689/100 = - (689 × 5)/(100 × 5) = - 3,445/500

Of course, the above fractions are reducing...


... to the initial fraction: - 689/100


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) negative improper fraction:
- 6.89 = - 689/100

As a mixed number:
- 6.89 = - 6 89/100

As a percentage:
- 6.89 = - 689%

As equivalent fractions:
- 6.89 = - 689/100 = - 2,756/400 = - 3,445/500

More operations of this kind

- 6.9 = ?

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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) fractions / theory:

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


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


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


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers