How to Convert Decimals to Fractions

Converting decimals into fractions isn’t hard. To convert a decimal into a fraction, you put the numbers to the right of the decimal point in the numerator (above the fraction line). Next, you place the number 1 in the denominator, and then add as many zeroes as the numerator has digits. Reduce the fraction if needed.

Decimals are nothing more than glorified fractions. They’re special because their denominators are always 10, 100, 1000, and so on — powers of 10. Watch where the decimal point is placed in the number. The number of decimal places to the right of the decimal point indicates the number of zeros in the power of 10 that is written in the denominator.

Example: Convert 3.025 to a fraction.

  1. Check to see if there is a number before (to the left of) the decimal.If there is, this number is the whole number of the fraction. So, 3 is the whole number.

  2. Place the number that falls after (to the right of) the decimal in the numerator; then use the decimal placement to determine the denominator.Place the number 1 in the denominator, and then add as many zeroes as the numerator has digits.A digit is any single number from 0 through 9.
    image

  3. Reduce the fraction.

Check out the decimal-to-fraction conversion in the following examples:

  • .3 has just one digit (3) to the right of the decimal point, so .3 becomes the fraction
    image

  • .408 has three digits (408) to the right of the decimal point, so .408 becomes the fraction
    image

  • 60.0003 has four digits (0003) to the right of the decimal point, but it also has a number that falls before the decimal, which becomes the whole number of the fraction. So 60.0003 becomes the fraction
    image

What are the rational number? Difference between rational and irrational numbers? Learn about terminating and repeating decimals? And How to convert decimals into fractions?

The numbers on which we perform calculation are of two categories, rational and irrational. Irrational is the numbers that cannot change into decimals, but rational numbers can be. So, let’s discuss rational numbers into decimals.

What are rational number?

Rational numbers are the numbers that can be written in p/q form, p and q can be any numbers or integers but q≠0. You can also say that rational numbers are a ratio of 2 digits; the same number is divided by the same number.
Capture1
Let’s suppose the numbers are not integers, how to convert them into ratio? Like 3.75

Difference between rational and irrational numbers?

Rational are numbers that are in p/q form, p and q can be any numbers but q≠0. They can be terminal, non terminal and recurring decimals. But irrational are the numbers that cannot be in p/q form. Numbers like π=3.1415926…, е=2.7182812…, Ф=1.618033…, √2=1.41421356… etc. are irrational numbers. Irrational numbers include imperfect square, non-terminating and non-recurring decimals.

Terminating and repeating decimals:

  1. Terminating decimals:
    Terminating decimals are finite number or group of numbers that finishes itself.

  2. Non-terminating decimals:
    Nonterminating decimals can never be finished, and not forming in repeating form. There can never be in fraction.

  3. Repeating and recurring decimals:
    Repeating decimals are a number and groups of numbers, are repeating and non-terminating. They can easily be converted into a fraction.

In short,decimals that can convert into fractions are:

  • Terminating and non-repeating
  • Non-terminating and repeating.

How to convert decimals into fractions?

• Converting a single digit decimal into fraction:

Let’s take an example of decimal digit 0.5, you can see that there is a single digit after point. So, you can just ease the point and then divide it with 10 (there is 1 digit after decimal so we add one zero (10) and divide it with 5). It is 5 of the fraction of one-tenth. To calculate the fraction, we just simply reduce it.
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• Converting Terminating and non-repeating decimal into fraction:

Terminal means that it must have a finite number of digits that are non-repeating.
Let’s see, how they are converting.
Capture3

• Converting Non-terminating and repeating decimal into fraction:

Non-Terminal means that it must have an infinite number of digits that are repeating.
Let’s see, how they are converting. Take an example.

To convert a decimal into a fraction: you must know about these tips.

4 Tips to convert a decimal into a fraction.

1. Convert 1.0 into fraction:

You can use this formula : N / N
                                              where N is a set of natural Number
let’s take an example:

  • if N= 2 put it into formula
  • N / N = 2 / 2 = 1

2. Convert 0.25 into a fraction:

You can use this formula : N / (N x 4)
                                              where N is a set of natural Number
let’s take an example:

  • if N= 2 put it into formula
  • N / (N x 4) = 2 / 2 x 4 = 2 /8 = 1 / 4
  • 0.25 = 1/ 4 in fraction.

3. Convert 0.5 into fraction:

You can use this formula : N / (N x 2)
                                              where N is a set of natural Number
let’s take an example:

  • if N= 2 put it into formula
  • N / (N x 2) = 2 / 2 x 2= 2 /4 = 1 / 2
  • 0. 5 = 1/ 2 in fraction.

4. Convert 0.75 into a fraction:

You can use this formula : (N x 3) / (N x 4)
                                              where N is a set of natural Number
let’s take an example:

  • if N= 2 put it into formula
  • (N x 3) / (N x 4) = (2 x 3) /( 2 x 4)= 6 /8 = 3 / 4
  • 0. 75 = 3 / 4 in fraction.
    decimal to fraction

To convert decimal into a fraction, try to use this formula.
As you know that fraction is always in Numerator and denominator form. OR p/q form.
This formula is for all type of decimal to fraction conversion equation.

                                           formula

Let’s take an example:

Convert 65.96 into decimal.

example

  • In this example: first calculate the value of x and y than put into the equation.
  1. Remove the decimal point and this is x; x= 6596
  2. Count the numbers after the decimal point that is y; y= 2
  3. Put into the formula: Capture2
  • As you see that this will be the fraction; and by reducing it, you can find the exact fraction in reducible form.

To convert decimal into a fraction, there are three possible situations:
Three steps:
1. First, count the numbers of digit after the decimal.

2. As you know that fraction is in numerator/denominator form so,
Remove the point from decimal value and put it in the numerator and write 1 in the denominator and put zeros equals to the count of digit after decimal with 1.

3. reduce the fraction and it gives you the exact answer.

try this, as it is the easiest way of conversion of decimal into a fraction.