Understanding everything about fraction to decimal


The process of converting a number expressed in the form of p/q, where p and q are whole numbers and q is not equal to 0, into decimal form may be characterised as either changing the denominator to a power of 10 or using the long division technique. In this post, we’ll look at various methods for converting fractions to decimals.

Fraction to Decimal Conversion

Any dividing fractions represented number is split into two components, the numerator and denominator. In general, we divide the numerator by the denominator to convert a fraction to decimal form. Fractions are written as p/q, where q0 is the unit of measurement. Decimal numbers, on the other hand, are constructed by joining the entire number and fractional parts through a decimal point, as in 7.575. Let’s look at some additional examples to better grasp the fraction to decimal conversion.

Converting Fractions to Decimals

Here’s an example of how to convert fractions to decimals in real life. Emma cuts her cardboard into 12 equal halves. She painted various coloured flowers on each piece of cardboard. She set aside 5 equal pieces of the 12 spaces for red flowers, 3 portions for green flowers, and 4 portions for orange flowers. Let’s write the portion allotted to each hue of flower in both fractional and decimal form.

  • The 5/12 or 0.4166 section of the cardboard is decorated with red flowers.
  • The 3/12 or 0.25 section of the cardboard is painted with green flowers.
  • The 4/12 or 0.333 section of the cardboard is likewise decorated with orange flowers.

Long Division Method to Convert Fractions to Decimals

When a number is in fraction form, such as p/q, the long division method is used to convert it to decimal form. In this example, the numerator is divided by the denominator. With the assistance of an example, let’s look at the stages involved in converting a fraction to a decimal using the long division approach.

Calculate the decimal equivalent of 4/19.

  • Step 1: Consider the numerator 4 as a dividend and the denominator 19 as the divisor in the provided fraction 4/19. In this example, the denominator is greater than the numerator.
  • Step 2: By putting a 0 next to 4 and the quotient, we can make the dividend digit (4) bigger than the numerator digit (19). We now have a fresh dividend of 40. (40>19)
  • Step 3: After the 0 in the quotient portion, enter a decimal (.) and begin the division.
  • Step 4: Multiply 19 by a number to get a result that is less than or equal to 40. We know that 19 divided by 2 equals 38. The remainder is 2, and the digit that occurred in the quotient is 2. We can insert one 0 at each stage of division after introducing decimal in the quotient.
  • Step 5: The new dividend is now twenty dollars. Multiply 19 by a number to get a result that is less than or equal to 20. 1 multiplied by 19 equals 19. The remainder is 1 and the new digit in the quotient is 1, making it 0.21.
  • Step 6: Repeat the steps until the residual is 0 or the quotient has at least three decimal places.

Change the denominator to convert a fraction to a decimal.

Another way to convert a fraction to a decimal is to change the denominator to powers of ten, such as 10, 100, 1000, and so on. The methods below demonstrate how to convert fractions to decimals using the converting the denominator approach.

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Convert 7/8 to decimals, for example.

  • Step 1: To acquire a power of 10 in the denominator, we must first conceive of a number by which we may multiply the denominator and numerator.
  • Step 2: The denominator in this case is 8. 8 times 125 equals 1000
  • Step 3: Multiply the numerator and denominator by the same amount, which is 125 in this case.
  • Step 4: We get 7 125 = 875 by multiplying the numerator of the fraction by 125.
  • Step 5: We now have a denominator in terms of the power of ten, i.e. 875/1000, after finishing the multiplication operation.
  • Step 6: In the denominator, insert a decimal point before the number of places equal to zeros. We add the decimal point before three places counting from the right side because the denominator has three zeros. As a result, we have 875/1000 = 0.875.

This approach is only relevant to fractions having a denominator that can be multiplied by a number to produce a power of ten. When the denominator cannot be represented as a power of ten, such as 2/3, it is always preferable to use the right concept guidance. Enrol in Cuemath classes and you will learn the best way to solve these equations. 

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