The relationship in between fractions and decimals is really important to know to build a strong base in arithmetic. Once a number is represented in type of p/q, whereby p and also q belong to totality numbers and q is no equal to 0, it is termed as a fraction and deserve to be converted into a decimal type by either converting the denominator to a strength of 10 or by long department method.

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

## What is the Relationship between Fractions and Decimals?

Bothfractionsanddecimalsare just two ways to represent numbers. Fractions are written in the form ofp/q, whereq≠0, while in decimals, the whole number part and fractional component are associated through adecimal point, because that example,0.5. Fractions and also decimals stand for the relationship of part by whole. In both fractions and also decimals, we represent the entirety by1. Let us look at some examples to understand the relationship between fractions and also decimals. Think about a full-thin tardy pizza with 6 slices. Your mom gave half of it, i.e., 3 slices then in fractional form, we compose it as1/2, and in the decimal form, we compose it as0.5.

Let united state consider one more example. Emma divides her garden right into 12 equal parts. She grows flower of various colors in each part of the garden. Among the 12 slots, she scheduled 8 equal portionsfor red flowers, 2 sections for yellow shade flowers, and 2 because that blue shade flowers. Let us write the section given to flower of each shade in fraction and in decimal.

Redflowers are grown in the 8/12 or0.666partof the garden.Yellow flowers are 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 us look at the portion and decimal representation given in the chart listed below to have an ext clarity around the fractions and decimals relationship. ## Converting portion into Decimal

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

Long department MethodConvert the denominator the the portion to multiples of 10 favor 10, 100, 1000, etc.

### Converting fraction to Decimal by Long department Method

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

Convert 3/8 into decimals.

Step 1: Treatthe numeratordigit of the fraction as a dividend and the denominator together the divisor.In this case, the numerator is lesser 보다 the denominator.Step 2: make the dividend better than the numerator by placing 0 beside the digit and also to the quotient. Now we have actually 30 together a new dividend. (30>8).Step 3: In the quotient,place decimal after 0 and start the division.Step 4: multiply 8 v a number so that the product is much less than same to 30. 8 time 3 is 24. Right here 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 new dividend is 60. Main point 8with a number so the the product is less than equal to 60.8 time 7is 56.Here currently quotient is 7, the remainder is 4.Step 6:Now the brand-new dividend is 40. Multiply 8with a number so that the product is less than same 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 method to convert the portion to a decimal is through convertingthe denominator that the fraction to powers of 10 prefer 10, 100, 1000, etc. Let us know this through the steps given below. We will certainly take an instance to proceed with the given steps.

Convert 3/4 come decimals.

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

Every decimal number can be to express in the kind of afraction. Procedures to convert a decimal number come the fractional form are proclaimed below:

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

Look in ~ 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 boundless values along with finite values.For example, if we convert the above fraction todecimal, us get0.33333333 and also it walk on approximately infinity.

### Related Articles

Check the end the web links of interesting posts related to the relationship between fractions and also decimals.

Example 1. Because that the complying with figure, what is the decimal representation of the orange shaded portion of the bluesquare? Solution:

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

1/4×25/25=25/100=0.25

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

Example 2.Jackbought 1000orangesfrom a adjacent fruit vendor but later found out that 25of them to be rotten. Deserve to you phone call the portion and thedecimal worth of the rotten orangesto the total orangesbought by Jack?

Solution:

Here, we have actually 25rotten orangesout of1000. Therefore our portion becomes 25/1000. Exactly how do we compose it as a decimal?Such difficulties are solved by dividing the numerator by the denominator. Here, we must divide 25 through 1000. To divide 25 by 1000, we will certainly simply shift it by 3decimal places on the right. Below in the numerator, we have actually only 2 digits (25) so right here we will introduce one zero prior to 025. The decimal ar of the last answer depends upon the number of trailing zeros present in the number of the denominator. Thus, after division, we get:025/1000 = 0.025∴ The proportion of rotten orangesto new orangesin decimal kind is0.025

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

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Solution:

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