Convert the pure repeating (recurring) decimal number 0.037. Turn it into a reduced (simplified) proper fraction and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

Convert 0.037

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

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

0.0370.03703703703704


Multiply the number by 100/100.

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

Note: 100/100 = 1


0.03703703703704 =


0.03703703703704 × 100/100 =


(0.03703703703704 × 100)/100 =


3.703703703704/100 =


3.703703703704% ≈


3.7%


(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, %


0.0373.7%



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

0.037 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 = 0.037


Set up the second equation.

Number of decimal places repeating: 3

Multiply both sides of the first equation by 103 = 1,000


y = 0.037


1,000 × y = 1,000 × 0.037


1,000 × y = 37.037


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.


1,000 × y - y = 37.037 - 0.037


(1,000 - 1) × y = 37.037 - 0.037


We now have a new equation:


999 × y = 37


Solve for y in the new equation.

999 × y = 37 ⇒


y = 37/999


Let the result written as a fraction.



Write the number as a fraction.

According to our first equation:

y = 0.037


According to our calculations:

y = 37/999


⇒ 0.037 = 37/999


3. Reduce (simplify) the fraction above: 37/999
(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):


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


999 = 33 × 37



Calculate the greatest (highest) common factor (divisor), GCF.

Multiply all the common prime factors by the lowest exponents.

GCF (37; 33 × 37) = 37



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

37/999 =


37/(33 × 37) =


(37 ÷ 37) / ((33 × 37) ÷ 37) =


1/33 =


1/27


1/27: 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 3:

1/27 = (1 × 3)/(27 × 3) = 3/81

Example 2. By expanding the fraction by 6:

1/27 = (1 × 6)/(27 × 6) = 6/162

Of course, the above fractions are reducing...


... to the initial fraction: 1/27



:: Final answer ::
Written in 3 different ways

As a reduced (simplified) positive proper fraction:
0.037 = 1/27

As a percentage:
0.037 ≈ 3.7%

As equivalent fractions:
0.037 = 1/27 = 3/81 = 6/162

More operations of this kind

0.038 = ? Convert the pure repeating (recurring) decimal number 0.038. 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

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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.

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