Convert the pure repeating (recurring) decimal number 800.5005. 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 800.5005

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

Approximate to the desired number of decimal places:

800.5005 ≈ 800.5005500550055


Multiply the number by 100/100.

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

Note: 100/100 = 1


800.5005500550055 =

800.5005500550055 × 100/100 =

(800.5005500550055 × 100)/100 =

80,050.05500550055/100 =

80,050.05500550055% ≈

80,050.06%

(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, %

800.5005 ≈ 80,050.06%


Convert fractions to percentages, online calculator


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

800.5005 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 = 800.5005


Set up the second equation.

Number of decimal places repeating: 4

Multiply both sides of the first equation by 104 = 10,000


y = 800.5005

10,000 × y = 10,000 × 800.5005

10,000 × y = 8,005,005.5005


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.


10,000 × y - y = 8,005,005.5005 - 800.5005 =>

(10,000 - 1) × y = 8,005,005.5005 - 800.5005 =>

We now have a new equation:

9,999 × y = 8,004,205


Solve for y in the new equation.

9,999 × y = 8,004,205 =>

y = 8,004,205/9,999

Let the result written as a fraction.



Write the number as a fraction.

According to our first equation:

y = 800.5005

According to our calculations:

y = 8,004,205/9,999

=> 800.5005 = 8,004,205/9,999


3. Reduce (simplify) the fraction above: 8,004,205/9,999
(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):

8,004,205 = 5 × 11 × 145,531

9,999 = 32 × 11 × 101


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 (5 × 11 × 145,531; 32 × 11 × 101) = 11


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


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

8,004,205/9,999 =

(5 × 11 × 145,531)/(32 × 11 × 101) =

((5 × 11 × 145,531) ÷ 11) / ((32 × 11 × 101) ÷ 11) =

(5 × 145,531)/(32 × 101) =

727,655/909


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.


727,655 ÷ 909 = 800, remainder = 455 =>

727,655 = 800 × 909 + 455 =>

727,655/909 =

(800 × 909 + 455) / 909 =

(800 × 909) / 909 + 455/909 =

800 + 455/909 =

800 455/909


727,655/909: 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:

727,655/909 = (727,655 × 2)/(909 × 2) = 1,455,310/1,818

Example 2. By expanding the fraction by 3:

727,655/909 = (727,655 × 3)/(909 × 3) = 2,182,965/2,727

Of course, the above fractions are reducing...

... to the initial fraction: 727,655/909


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
800.5005 = 727,655/909

As a mixed number:
800.5005 = 800 455/909

As a percentage:
800.5005 ≈ 80,050.06%

As equivalent fractions:
800.5005 = 727,655/909 = 1,455,310/1,818 = 2,182,965/2,727

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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