The relationship between fractions and decimals is really important to recognize to build a strong base in arithmetic. As soon as a number is represented in type of p/q, whereby p and q belong to totality numbers and also q is not equal come 0, it is termed as a fraction and have the right to be converted into a decimal form by one of two people converting the denominator come a strength of 10 or through long department method.

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1.What is the Relationship in between Fractions and also Decimals?
2.Converting fraction into Decimal
3.Converting Decimal into Fraction
4.Solved Examples
5.Practice Questions
6.FAQs ~ above Relationship between Fractions and also Decimals

What is the Relationship between Fractions and Decimals?

Bothfractionsanddecimalsare simply two ways to stand for numbers. Fractions space written in the type ofp/q, whereq≠0, while in decimals, the totality number part and fractional component are connected through adecimal point, because that example,0.5. Fractions and also decimals stand for the partnership of part by whole. In both fractions and also decimals, we stand for the totality by1. Let united state look at some examples to know the relationship in between fractions and also decimals. Take into consideration a full-thin late pizza with 6 slices. Your mother gave fifty percent of it, i.e., 3 slices then in fountain form, we compose it as1/2, and in the decimal form, we compose it as0.5.

Let us consider one more example. Emma divides her garden into 12 equal parts. She grows flower of various colors in each component of the garden. Amongst the 12 slots, she scheduled 8 same portionsfor red flowers, 2 parts for yellow shade flowers, and also 2 for blue shade flowers. Let us write the portion given to flower of each shade in portion and in decimal.

Redflowers room grown in the 8/12 or0.666partof the garden.Yellow flowers room grown in the 2/12 or 0.1666partof the garden.Blue flower are additionally grown in the 2/12 or 0.1666 partof the garden.

Let united state look at the fraction and decimal representation offered in the chart below to have more clarity around the fractions and decimals relationship.


Converting portion into Decimal

We can convert a portion to its decimal form by the following two methods.

Long department MethodConvert the denominator of the fraction to multiples the 10 prefer 10, 100, 1000, etc.

Converting fraction to Decimal by Long department Method

When a number is existing in a fraction type i.e., p/q, to convert it into the decimal kind we use the long division method. The measures for convert fractions right into decimals are offered below.Let us know these procedures of the long division with the assist of one example.

Convert 3/8 right into decimals.

Step 1: Treatthe numeratordigit the the portion as a dividend and also the denominator as the divisor.In this case, the numerator is lesser than the denominator.Step 2: make the dividend better than the molecule by put 0 next to the digit and also to the quotient. Now we have 30 together a brand-new dividend. (30>8).Step 3: In the quotient,place decimal after 0 and also start the division.Step 4: multiply 8 through a number so the the product is much less than equal to 30. 8 times 3 is 24. Below now the digit in the quotient is 3, the remainder is 6. After presenting decimal in the quotient us can connect one 0 in ~ each step of division.Step 5: currently the brand-new dividend is 60. Multiply 8with a number so that the product is less than equal to 60.8 times 7is 56.Here now quotient is 7, the remainder is 4.Step 6:Now the new dividend is 40. Multiply 8with a number so the the product is much less than same to 40.8 times 5is 40.Step 7: The final remainder is 0 and also the quotient is 0.375.3/8 = 0.375.


Convert the Denominator

Another technique to transform the portion to a decimal is by convertingthe denominator of the portion to strength of 10 prefer 10, 100, 1000, etc. Let us know this v the steps given below. We will take an example to continue with the offered steps.

Convert 3/4 come decimals.

Step1: Think that a number through which we can easily multiply the denominator and numerator to acquire the strength of 10.Step2: below denominator is 4. 4 time 25 is 100.Step 3: multiply the numerator likewise with the same numberStep 4: By multiplying the numeratorof the fraction by 25 we gain (3× 25) = 75Step 5: currently we have actually a denominator in terms of powers of 10.Step 6: 75/100 = 0.75.The decimal location of the last answer relies upon the variety of trailing zeros existing inthe number of thedenominator.

Every decimal number can be expressed in the form of afraction. Procedures to transform a decimal number come the fractional type are declared below:

Rewrite the number by skipping the decimal point.Simplify the fraction.

Look in ~ this example for a depth understanding.

Decimal type = 6.5 = 65/10 = 13/2 (Fraction type of 6.5)

Important Notes:

Decimals can likewise represent infinite values in addition to finite values.For example, if we transform the above fraction todecimal, we get0.33333333 and also it goes on as much as infinity.

Related Articles

Check the end the web links of interesting write-ups related come the relationship in between fractions and also decimals.

Example 1. For the following figure, what is the decimal representation of the orange shaded portion of the bluesquare?



Itisgiven that, 1 the end of 4 blue-colored squares is shaded orange. So, the fraction of the orange shaded part tothe blue square is1/4. To transform it into a decimal, we need to multiply both numerator and also denominator by25, therefore that us will have a power of 10 in the denominator.


Therefore, 0.25or1/4 part of the bluesquare is shaded orange.

Example 2.Jackbought 1000orangesfrom a adjacent fruit seller but later discovered out that 25of them to be rotten. Have the right to you phone call the fraction and thedecimal value of the rotten orangesto the complete orangesbought by Jack?


Here, we have 25rotten orangesout of1000. So our fraction becomes 25/1000. How do we create it as a decimal?Such troubles are solved by separating the molecule by the denominator. Here, we should divide 25 by 1000. To division 25 through 1000, we will simply shift it through 3decimal places on the right. Below in the numerator, we have only 2 number (25) so below we will present one zero before 025. The decimal location of the last answer counts upon the number of trailing zeros current in the number of the denominator. Thus, after division, us get:025/1000 = 0.025∴ The proportion of rotten orangesto fresh orangesin decimal type is0.025

Example 3:There are36fruits in a basket.9are mangoes and also the remaining are apples. What fractionof the fruits space apples? compose your answer in decimal too.

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Total variety of fruits in the basket =36Number that mangoes =9Number of apples =36 − 9 = 27 apples∴The portion of apples in the basket is27/36and in simplest form,3/4Now, we need to convert3/4into decimal.To convert3/4into decimal, we multiply both numerator and denominator by25to get a power of 10 in the denominator.=3/4×25/25=75/100=0.75∴0.75or3/4fruits in the basket space apples.