The relationship in between fractions and decimals is really important to understand to construct a solid base in arithmetic. As soon as a number is stood for in kind of p/q, where p and also q belong to entirety numbers and q is not equal to 0, the is termed together a portion and deserve to be converted right into a decimal form by either converting the denominator to a power of 10 or by long department method.

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

What is the Relationship between Fractions and also Decimals?

Bothfractionsanddecimalsare simply two means to stand for numbers. Fractions are written in the type ofp/q, whereq≠0, while in decimals, the totality number component and fractional part are linked through adecimal point, because that example,0.5. Fractions and decimals stand for the partnership of part by whole. In both fractions and decimals, we represent the entirety by1. Let us look in ~ some examples to know the relationship in between fractions and decimals. Take into consideration a full-thin crust pizza with 6 slices. Your mommy gave half of it, i.e., 3 slices then in fractional form, we create it as1/2, and also in the decimal form, we compose it as0.5.

Let united state consider another example. Emma divides her garden into 12 same parts. She grows flower of various colors in each component of the garden. Amongst the 12 slots, she reserved 8 same portionsfor red flowers, 2 sections for yellow color flowers, and also 2 for blue shade flowers. Let us write the portion given to flowers of each color in fraction and in decimal.

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

Let united state look in ~ the portion and decimal representation offered in the chart listed below to have much more clarity about the fractions and also decimals relationship.


Converting portion into Decimal

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

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

Converting portion to Decimal by Long department Method

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

Convert 3/8 right into decimals.

Step 1: Treatthe numeratordigit that the portion as a dividend and the denominator as the divisor.In this case, the numerator is lesser than the denominator.Step 2: make the dividend better than the numerator by place 0 next to the digit and to the quotient. Now we have 30 together a brand-new dividend. (30>8).Step 3: In the quotient,place decimal ~ 0 and also start the division.Step 4: main point 8 through a number so that the product is much less than equal to 30. 8 time 3 is 24. Right here now the digit in the quotient is 3, the remainder is 6. After introducing decimal in the quotient we can affix one 0 in ~ each action of division.Step 5: now the 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 brand-new dividend is 40. Main point 8with a number so that the product is much less than equal to 40.8 times 5is 40.Step 7: The final remainder is 0 and the quotient is 0.375.3/8 = 0.375.


Convert the Denominator

Another an approach to convert the portion to a decimal is by convertingthe denominator the the fraction to strength of 10 favor 10, 100, 1000, etc. Let us know this with the steps offered below. We will take an example to continue with the provided steps.

Convert 3/4 come decimals.

Step1: Think the a number through which we can conveniently multiply the denominator and numerator to gain the power of 10.Step2: here denominator is 4. 4 time 25 is 100.Step 3: multiply the numerator likewise with the exact same numberStep 4: By multiplying the numeratorof the portion by 25 we obtain (3× 25) = 75Step 5: now we have a denominator in regards to powers that 10.Step 6: 75/100 = 0.75.The decimal location of the last answer counts upon the variety of trailing zeros existing inthe number of thedenominator.

Every decimal number deserve to be to express in the form of afraction. Measures to convert a decimal number to the fractional kind are declared below:

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

Look at this example for a depths understanding.

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

Important Notes:

Decimals can additionally represent unlimited values in addition to finite values.For example, if we convert the above portion todecimal, we get0.33333333 and also it go on up to infinity.

Related Articles

Check out the web links of interesting articles related to the relationship in between fractions and decimals.

Example 1. Because that the following figure, what is the decimal representation of the orange shaded section of the bluesquare?



Itisgiven that, 1 the end of 4 blue-colored squares is shaded orange. So, the portion of the orange shaded portion tothe blue square is1/4. To convert it into a decimal, we have to multiply both numerator and denominator by25, for this reason that we will have actually a strength of 10 in the denominator.


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

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


Here, we have actually 25rotten orangesout of1000. Therefore our portion becomes 25/1000. How do we compose it together a decimal?Such troubles are fixed by separating the molecule by the denominator. Here, we must divide 25 by 1000. To division 25 by 1000, we will certainly simply transition it through 3decimal locations on the right. Right here in the numerator, we have actually only 2 digits (25) so right here we will present one zero before 025. The decimal ar of the last answer counts upon the variety of trailing zeros current in the digit of the denominator. Thus, after ~ division, we get:025/1000 = 0.025∴ The proportion of rotten orangesto fresh orangesin decimal kind is0.025

Example 3:There are36fruits in a basket.9are mangoes and the remaining are apples. What fractionof the fruits are apples? write your price in decimal too.

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