Convert the mixed repeating (recurring) decimal number 0.00005. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Equivalent fractions calculator

Convert 0.00005 into equivalent fractions and write it as a percentage value

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

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

0.00005 ≈ 0.00005555555556


Multiply the number by 100/100.

  • The value of the number does not change when multiplying by 100/100.
  • Note: 100/100 = 1

0.00005555555556 =

0.00005555555556 × 100/100 =

(0.00005555555556 × 100)/100 =

0.005555555556/100 =

0.005555555556% ≈

0.01%

(rounded off to max. 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, %
  • 0.00005 ≈ 0.01%

» Convert fractions to percentages, online calculator


2. Write the mixed repeating (recurring) decimal number as a proper fraction.

  • 0.00005 can be written as a proper fraction.

  • The numerator is smaller than the denominator.

Set up the first equation.

  • Let y equal the decimal number:

  • y = 0.00005


Set up the second equation.

  • Number of decimal places repeating: 1

  • Multiply both sides of the first equation by 101 = 10


y = 0.00005

10 × y = 10 × 0.00005

10 × y = 0.0005

Get the same number of decimal places as for y:

10 × y = 0.00055

Note: 0.00055 = 0.0005


Subtract the first equation from the second one.

  • Having the same number of decimal places ...
  • The repeating pattern drops off by subtracting the two equations.

10 × y - y = 0.00055 - 0.00005 ⇒

(10 - 1) × y = 0.00055 - 0.00005 ⇒

We now have a new equation:

9 × y = 0.0005


Solve for y in the new equation.

9 × y = 0.0005 ⇒

y = 0.0005/9

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 0.00005

According to our calculations:

y = 0.0005/9

⇒ 0.00005 = 0.0005/9


Get rid of the decimal places in the fraction above.

  • Multiply the top and the bottom number by 10,000.
  • 1 followed by as many 0-s as the number of digits after the decimal point.

0.00005 = (0.0005 × 10,000)/(9 × 10,000)

0.00005 = 5/90,000


3. Reduce (simplify) the fraction above:
5/90,000
to the lowest terms, to its simplest equivalent form, irreducible.

To reduce a fraction to the lowest terms divide the numerator and denominator by their greatest (highest) common factor (divisor), GCF.


Factor the numerator and denominator (prime factorization).

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

90,000 = 24 × 32 × 54


» 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; 24 × 32 × 54) = 5


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


Divide both the numerator and the denominator by their GCF.

5/90,000 =

5/(24 × 32 × 54) =

(5 ÷ 5) / ((24 × 32 × 54) ÷ 5) =

1/(24 × 32 × 53) =

1/18,000


1/18,000 ~ 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 6.

1/18,000 = (1 × 6)/(18,000 × 6) = 6/108,000

Example 2. By expanding the fraction by 8.

1/18,000 = (1 × 8)/(18,000 × 8) = 8/144,000

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 1/18,000

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.00005 = 1/18,000

As a percentage:
0.00005 ≈ 0.01%

As equivalent fractions:
0.00005 = 1/18,000 = 6/108,000 = 8/144,000

More operations of this kind

0.00006 = ? Convert the mixed repeating (recurring) decimal number 0.00006. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

Decimal numbers to fractions and percentages, calculator

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.

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