Convert the decimal number 0.002. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

1. Write the number as a percentage.

Note: 100/100 = 1

0.002 =


0.002 × 100/100 =


(0.002 × 100)/100 =


0.2/100 =


0.2%


In other words:


Multiply the number by 100...


... And then add the percent sign, %


0.002 = 0.2%


Convert fractions to percentages, online calculator


2. Write the number as a proper fraction.

0.002 can be written as a proper fraction.

(The numerator is smaller than the denominator).

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

0.002 = 0.002/1

Turn the top number into a whole number.

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


This number is: 1,000.


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


0.002/1 =


(0.002 × 1,000)/(1 × 1,000) =


2/1,000


3. Reduce (simplify) the fraction above: 2/1,000
(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):


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


1,000 = 23 × 53

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 (2; 23 × 53) = 2

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


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

2/1,000 =


2/(23 × 53) =


(2 ÷ 2) / ((23 × 53) ÷ 2) =


1/(22 × 53) =


1/500


1/500: 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 3:

1/500 = (1 × 3)/(500 × 3) = 3/1,500

Example 2. By expanding the fraction by 4:

1/500 = (1 × 4)/(500 × 4) = 4/2,000

Of course, the above fractions are reducing...


... to the initial fraction: 1/500


Reduce fractions and write them as decimal numbers and percentages


:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.002 = 1/500

As a percentage:
0.002 = 0.2%

As equivalent fractions:
0.002 = 1/500 = 3/1,500 = 4/2,000

0.003 = ?

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:

  • 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) 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