Fraction to Decimal
The fraction to decimal is a type of conversion that can be defined as, the process of converting a number represented in form of p/q, where p and q belong to whole numbers and q is not equal to 0 into a decimal form by either converting the denominator to a power of 10 or by long division method. Let us see what are the different ways of converting the fractions to decimal more precisely in this article.
|1.||Fraction to Decimal Conversion|
|2.||How to Convert Fraction to Decimal?|
|3.||Fraction to Decimal Chart|
|4.||Fraction to Decimal Calculator|
|5.||FAQs on Fraction to Decimal|
Fraction to Decimal Conversion
Any number which is represented in a fraction form is divided into two parts i.e., numerator and denominator. Generally, to convert a number from fraction to decimal form we divide the numerator by the denominator.Fractions are represented in the form of q/p, where p≠0. While the decimal numbers are formed by connecting the whole number part and fractional part through a decimal point, for example, 7.575. Let us explore some more illustrations to understand the fraction to decimal conversion in detail.
Fraction to Decimal Conversion Example
Here is a real-life example to understand fraction to decimal conversion. Emma divides her cardboard into 12 equal parts. She painted the flowers of different colors on each part of the cardboard. Amongst the 12 slots, she reserved 5 equal portions for red color flowers, 3 portions for green color flowers, and 4 for orange color flowers. Let us write the portion given to flowers of each color in a fraction as well as in decimal form.
- Red color flowers are painted in the 5/12 or 0.4166 part of the cardboard.
- Green color flowers are painted in the 3/12 or 0.25 part of the cardboard.
- Orange color flowers are also painted in the 4/12 or 0.333 part of the cardboard.
Let us look at the fraction and decimal representation given in the chart below to have more clarity about the fraction to decimal conversion.
How to Convert Fraction to Decimal?
To convert a fraction to its decimal form by the following two methods.
- Long division method
- By converting the denominator of the fraction into the multiples of 10.
Fraction to Decimal Conversion by Long Division Method
When a number is present in a fraction form i.e., p/q, we use the long division method to convert it into a decimal form. In such a case we divide the numerator value by the denominator value. Let us understand the steps involved in fraction to decimal conversion by the long division with the help of an example.
Convert 4/19 fraction to decimals.
Step 1: In the given fraction 4/19, take the numerator digit 4 as a dividend and the denominator digit 19 as the divisor. In this case, the denominator > numerator.
Step 2: We have to make the dividend digit (4) greater than the numerator digit (19) by placing 0 next to the 4 and to the quotient respectively. Now we have 40 as a new dividend. (40>19).
Step 3: In the quotient part, it is important to insert decimal (.) after 0 and start the division.
Step 4: Multiply 19 with a number so that the product is less than equal to 40. 19 times 2 is 38. The digit that appeared in the quotient is 2, the remainder left is 2. After introducing decimal in the quotient we can introduce one 0 at each step of division.
Step 5: Now the new dividend is 20. Multiply 19 with a number so that the product is less than equal to 20. 19 times 1 is 19. Here now the quotient is 1 and the complete quotient is (0.21), the leftover remainder is 1.
Step 6: Repeat the steps till we get 0 as remainder or at least three decimal places in the quotient. Try to read out the steps with the image given below for having a better understanding of converting fractions to decimals.
In our next section, let us discuss another method of the fraction to decimal conversion that is by converting the denominator into multiples of 10.
By Converting the Denominator
Another method to convert the fraction to a decimal is by converting the denominator of the fraction to powers or multiples of 10 like 10, 100, 1000, etc. Following are the steps showing the procedure included in the conversion of fractions to decimals by converting the denominator method. Let us consider an illustration here to understand it with a practical approach.
Example: Convert 7/8 to decimals.
Step1: Firstly we have to think of a number by which we can easily multiply the denominator and numerator by such a number so that we can get a multiple or power of 10.
Step2: Here denominator is 8. (8 times 125 is 1000).
Step 3: Now multiply the numerator with the same number, i.e., 7 times 125
Step 4: By multiplying the numerator digit of the fraction by 125 we get (7 × 125) = 875
Step 5: After completing the multiplication process we have a denominator in terms of power or multiples of 10.
Step 6: Final result in terms of decimals we have, 875/1000 = 0.875.
Note that the decimal place of the final answer depends upon the number of trailing zeros present in the digit of the denominator.
Fraction to Decimal Chart
Fraction to decimal chart is a direct approach to get the converted values easily. The chart gives us the values of some most commonly used fractions in terms of decimals and vice-versa. Fractions can be less than or greater than 1. Fractions that are less than 1 have a numerator < denominator. They are called proper fractions. Fractions that have a numerator > denominator are called improper fractions. Let us have more clarity about how the numbers will look like when we convert fractions to decimal form. Check out our specific page on the fraction to the decimal chart for proper understanding.
Fraction to Decimal Calculator
Check our fraction to decimal calculator and try few conversions at your end. It is a free online tool that calculates the decimal form of a given fraction. Our calculator helps you to calculate the decimal value of fractions within a few seconds.
☛ Related Articles
Given below is the list of topics that are closely connected to the fraction to decimals. These topics will also give you a glimpse of how such concepts are covered in Cuemath
Converting Fraction to Decimal Examples
Example 1. Convert the following fraction to decimal.
a) To convert 77/80 we will divide the numerator by the denominator. On dividing, 77 by 80 we get ⇒ 77/80 = 0.9625.
b) To convert the 12/16 fraction into decimal we will divide the numerator 12 by the denominator 16. On dividing, 12 by 16 we get ⇒ 12/16 = 0.75.
c) On converting 13/8 fraction into decimal we get ⇒ 13/8 = 1.625.
Example 2. Ron bought 150 bananas from a nearby fruit vendor but later found out that 50 of them were rotten. Can you tell the fraction and the decimal value of the rotten bananas to the total bananas bought by Ron?
Number of bananas = 150
Number of rotten bananas = 50
So our fraction becomes = 50/150.
To convert the fraction to decimal in this case, we will divide the numerator by the denominator.
Divide 50 by 150.
Thus, after division, we get:
50/150 = 0.333
∴ The ratio of rotten bananas to fresh bananas in decimal form is 0.333
Example 3: There are 80 cookies in a basket. 73 are choco chips cookies and the remaining are basic cookies. What fraction of the cookies are basic? Using fraction to decimal calculator write your answer in decimal.
Total number of cookies = 80
Number of choco chips cookies = 73
Number of basic cookies = 80 − 73 = 7 basic cookies
∴ The fraction of basic cookies is 7/80
Now, we have to convert 7/80 into decimal.
To convert 7/80 fraction into decimal, we multiply both numerator and denominator by 125 to get a power of 10 in the denominator.
∴ 0.0875 or 7/80 cookies in the lot are basic.
FAQs on Fraction to Decimal
What is the Fraction to Decimal Conversion in Math?
Fraction to decimal in math is referred to as a procedure that we generally used to convert the fraction value to decimal value. While converting a fraction to a decimal, we divide the parts of fractions, i.e., the numerator is divided by the denominator. Decimal gives a more precise value as compared to fractions.
To read the reverse conversion check now Decimal to Fraction Conversion.
How are Fractions to Decimals Conversion Represented?
Fractions are written in the form of p/q, where q≠0, while in decimals, the fractional part and the whole number part are connected through a decimal point, for example, 0.5.
How to Convert a Fraction to a Decimal?
To convert a fraction to a decimal, we need to follow the steps given below.
- The numerator of the fraction will be treated as a dividend and the denominator as the divisor.
- If the numerator is < denominator add a decimal (point) along with 0 after the dividend.
- Perform the division.
- If the remainder keeps recurring, then the decimal can be stopped after a certain number of decimal places.
- For example, converting 4/5 to decimal gives 0.8.
What is the Result of Converting fraction 22/7 to Decimals?
22/7 is an irrational number with 22 as the numerator and 7 as the denominator. On converting 22/7 into decimals we get 3.14 up to two decimal places. It is a non-terminating, non-repeating decimal number that extends up to infinity.
How to Convert 2/3 into Decimal Using the Fraction to Decimal Chart?
Using the fraction to decimal chart, the value of 2/3 is 0.666. To find the decimal value of 2/3 we perform the division operation until the remainder is 0 or up to 3-4 decimal places.
What Method is Used to Convert a Fraction to a Decimal?
The very easy and convenient method for converting a fraction to a decimal is by dividing the numerator by the denominator will convert a fraction to a decimal.
How to Convert a Mixed Fraction to Decimal?
To convert a mixed fraction to a decimal, we first need to convert it into an improper fraction. Then divide the numerator by denominator to convert it into decimal value.
☛ Read the following articles for basics: