Convert the pure repeating (recurring) decimal number 0.000000003. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Equivalent fractions calculator

Convert 0.000000003 into equivalent fractions and write it as a percentage value

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

Approximate to the desired number of decimal places.

0.000000003 ≈ 0.000000003


Multiply the number by 100/100.

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

0.000000003 =

0.000000003 × 100/100 =

(0.000000003 × 100)/100 =

0.0000003/100 =

0.0000003% ≈

0%

(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, %
  • 0.000000003 ≈ 0%

» Convert fractions to percentages, online calculator


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

  • 0.000000003 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 = 0.000000003


Set up the second equation.

  • Number of decimal places repeating: 9

  • Multiply both sides of the first equation by 109 = 1,000,000,000


y = 0.000000003

1,000,000,000 × y = 1,000,000,000 × 0.000000003

1,000,000,000 × y = 3.000000003


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.

1,000,000,000 × y - y = 3.000000003 - 0.000000003 ⇒

(1,000,000,000 - 1) × y = 3.000000003 - 0.000000003 ⇒

We now have a new equation:

999,999,999 × y = 3


Solve for y in the new equation.

999,999,999 × y = 3 ⇒

y = 3/999,999,999

Let the result written as a fraction.



Now we can write the number as a fraction.

According to our first equation:

y = 0.000000003

According to our calculations:

y = 3/999,999,999

⇒ 0.000000003 = 3/999,999,999


3. Reduce (simplify) the fraction above:
3/999,999,999
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).

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

999,999,999 = 34 × 37 × 333,667


» 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 (3; 34 × 37 × 333,667) = 3


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


Divide both the numerator and the denominator by their GCF.

3/999,999,999 =

3/(34 × 37 × 333,667) =

(3 ÷ 3) / ((34 × 37 × 333,667) ÷ 3) =

1/(33 × 37 × 333,667) =

1/333,333,333


1/333,333,333 ~ 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.

1/333,333,333 = (1 × 2)/(333,333,333 × 2) = 2/666,666,666

Example 2. By expanding the fraction by 6.

1/333,333,333 = (1 × 6)/(333,333,333 × 6) = 6/1,999,999,998

  • Of course, the above fractions are reducing...
  • ... to the initial fraction: 1/333,333,333

» Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.000000003 = 1/333,333,333

As a percentage:
0.000000003 ≈ 0%

As equivalent fractions:
0.000000003 = 1/333,333,333 = 2/666,666,666 = 6/1,999,999,998

More operations of this kind

0.000000004 = ? Convert the pure repeating (recurring) decimal number 0.000000004. 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.

More on ordinary (common) fractions / theory: