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Converting Decimals to Fractions

In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps:

Step I: Obtain the decimal.

Step II: Remove the decimal points from the given decimal and take as numerator.

Step III: At the same time write in the denominator, as many zero or zeros to the right of 1(one) (For example 10, 100 or 1000 etc.) as there are number of digit or digits in the decimal part. And then simplify it.

We can express a decimal number as a fraction by keeping the given number as the numerator without a decimal point and writing 1 in the denominator followed by as many zeroes on the right as the number of decimal places in the given decimal number has.

For example:                                                                           

(i) 124.6 = \(\frac{1246}{10}\)

(ii) 12.46 = \(\frac{1246}{100}\)

(iii) 1.246 = \(\frac{1246}{1000}\)


The problem will help us to understand how to convert decimal into fraction.

In 0.7 we will change the decimal to fraction.

First we will write the decimal without the decimal point as the numerator.

Now in the denominator, write 1 followed by one zeros as there are 1 digit in the decimal part of the decimal number.

Convert Decimal into Fraction




= \(\frac{7}{10}\)

Therefore, we observe that 0.7 (decimal) is converted to \(\frac{7}{10}\) (fraction).


Working Rules for Conversion of a Decimal Into a Fraction:

To convert a decimal into fraction, we follow the following steps
Working Rules

Step I: Write the given number without decimal point as the numerator of the fraction.

Step II: Write 1 in the denominator followed by as many zeros as the number of decimal places in the given number.

Step III: Reduce the fraction into the lowest terms and if required change into mixed numeral.


Solved Examples on Converting Decimals to Fractions

1. Convert 6.75 into a fraction.

Solution:

Numerator of fraction = 675

Denominator of fraction = 100 (Because decimal places are 2, therefore, put 2 zeros after 1.)

So, 6.75 = \(\frac{625}{100}\)

             = \(\frac{625 ÷ 25}{100 ÷ 25}\)

             = \(\frac{27}{4}\)

             = 6\(\frac{3}{4}\)


2. Convert 924.275 into a fraction.

Solution:

Numerator of fraction = 924275

Denomination of fraction = 1000 (Because decimal places are 3, therefore, put 3 zeros after 1.)

Now, 924.275 = \(\frac{924275}{1000}\)

                     = \(\frac{924275 ÷ 25}{1000 ÷ 25}\)

                     = \(\frac{36971}{40}\)

                     = 924\(\frac{11}{40}\)


Worked-out Examples on Converting Decimals to Fractions:


1. Convert each of the following into fractions.

(i) 3.91

Solution:

3.91

Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros as there are 2 digits in the decimal part of the decimal number.

= \(\frac{391}{100}\)


(ii) 2.017

Solution:

2.017

= \(\frac{2.017}{1}\)

= \(\frac{2.017 × 1000}{1 × 1000}\)  In the denominator, write 1 followed by three zeros as there are 3 digits in the decimal part of the decimal number.

= \(\frac{2017}{1000}\)


2. Convert 0.0035 into fraction in the simplest form.

Solution:

0.0035

Fraction in the Simplest Form






Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by four zeros to the right of 1 (one) as there are 4 decimal places in the given decimal number.

Now we will reduce the fraction \(\frac{35}{10000}\) and obtained to its lowest term or the simplest form.

= \(\frac{7}{2000}\)


3. Express the following decimals as fractions in lowest form:

(i) 0.05

Solution:

0.05

= \(\frac{5}{100}\) Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.

= \(\frac{5 ÷ 5}{100 ÷ 5}\)  Reduce the fraction obtained to its lowest term.

= \(\frac{1}{20}\)


(ii) 3.75

Solution:

3.75

= \(\frac{375}{100}\)  Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.

= \(\frac{375 ÷ 25}{100 ÷ 25}\)  Reduce the fraction obtained to its simplest form.

= \(\frac{15}{4}\)


(iii) 0.004

Solution:

0.004

= \(\frac{4}{1000}\) Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.

= \(\frac{4 ÷ 4}{1000 ÷ 4}\) ⟹ Reduce the fraction obtained to its lowest term.

= \(\frac{1}{250}\)


(iv) 5.066

Solution:

5.066

= \(\frac{5066}{1000}\)  Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.

= \(\frac{5066 ÷ 2}{1000 ÷ 2}\)  Reduce the fraction obtained to its simplest form.

= \(\frac{2533}{500}\)


More Examples on Converting Decimals into Fractions:

Let us consider a few more examples for converting decimals into fractions

STEPS

Step I: Remove the decimal point and write the number as the numerator of the required fraction

Step II: Write 1 as denominator.

Step III: Count the number of digits to the right of the decimal point in the decimal and write the same number of zero to the right of 1 in the denominator


4. Convert 2.7 into a fraction

Solution:

27 = \(\frac{27}{10}\)

    = 2\(\frac{7}{10}\)

Therefore, 27 = 2\(\frac{7}{10}\)


5. Convert 32.47 into a fraction.

Solution:

32.47

The denominator will have two zeros to the right of 1 because the decimal has two digits to the right of the decimal point,

32.47 = \(\frac{3247}{100}\)

         = 32\(\frac{47}{100}\)

Therefore, 32.47 = 32\(\frac{47}{100}\)


6. Convert 2.255 into a fraction

Solution:

2.255 = \(\frac{2255}{1000}\);

         =  2255/1000 

[We always reduce the fraction to its lowest terms.]

         = \(\frac{451}{200}\)

         = 2\(\frac{51}{200}\)

Thus, 2.255 = 2\(\frac{51}{200}\)


7. Convert the following decimals into a fraction

(i) 425.25

(ii) 318.4

Solution:

(i) 425.25 = \(\frac{42524}{100}\)

                = 42525/100

[We always reduce the fraction to its lowest terms.]

               = \(\frac{1701}{4}\)

               = 425\(\frac{1}{4}\)

Thus, 425.25 = 425\(\frac{1}{4}\)


(ii) 318.4 = \(\frac{3184}{10}\)

              = 3184/10

[We always reduce the fraction to its lowest terms.]

              = \(\frac{1592}{5}\)

              = 318\(\frac{2}{5}\)

Thus, 318.4 = 318\(\frac{2}{5}\)

Converting Decimals to Fractions


Worksheet on Converting Decimals to Fractions:

1. Convert the given decimal numbers to fractions in the lowest term:

(i) 1.3

(ii) 0.004

(iii) 4.005

(iv) 7.289

(v) 0.56

(vi) 21.08

(vii) 0.067

(viii) 6.66


Answers:

1. (i) \(\frac{13}{10}\)

(ii) \(\frac{1}{250}\)

(iii) \(\frac{801}{200}\)

(iv) \(\frac{7289}{1000}\)

(v) \(\frac{14}{25}\)

(vi) \(\frac{527}{25}\)

(vii) \(\frac{67}{1000}\)

(viii) \(\frac{333}{50}\)


2. Convert the following decimals into common fractions in the lowest terms:

(i) 0.7

(ii) 0.15

(iii) 0.085

(iv) 27.35

(v) 0.27

(vi) 2.08

(vii) 17.2

(viii) 5.005

(ix) 206.007

(x) 0.003

(xi) 71.035

(xii) 35.607


Answer:

2. (i) \(\frac{7}{10}\)

(ii) \(\frac{3}{20}\)

(iii) \(\frac{17}{200}\)

(iv) 27\(\frac{7}{20}\)

(v)\(\frac{27}{100}\)

(vi) 2\(\frac{2}{5}\)

(vii) 17\(\frac{1}{5}\)

(viii) 5\(\frac{1}{200}\)

(ix) 206\(\frac{7}{1000}\)

(x) \(\frac{3}{1000}\)

(xi) 71\(\frac{7}{200}\)

(xii) 35\(\frac{607}{1000}\)


3. Convert into fractions.

(i) 0.3

(ii) 23.43

(iii) 0.9

(iv) 256.58

(v) 0.7

(vi) 423.35

(vii) 0.13

(viii) 621.524

(ix) 0.24

(x) 983.45

(xi) 2.11

(xii) 898.752

(xiii) 6.27

(xiv) 252.45

(xv) 0.368

(xvi) 4.32

(xvii) 52.35

(xviii) 417.125

(xix) 7.123

(xx) 15.21

(xxi) 12.425

(xxii) 151.141

(xxiii) 131.328

(xxiv) 95.171

(xxv) 29.24

(xxvi) 14.3

(xxvii) 64.25

(xxviii) 112.32

(xxix) 46.005

(xxx) 41.55


Answer:

3. (i) \(\frac{3}{10}\)

(ii) 23\(\frac{43}{100}\)

(iii) \(\frac{9}{10}\)

(iv) 256\(\frac{29}{50}\)

(v) \(\frac{7}{10}\)

(vi) 423\(\frac{7}{20}\)

(vii) \(\frac{13}{100}\)

(viii) 621\(\frac{131}{250}\)

(ix) \(\frac{6}{25}\)

(x) 983\(\frac{9}{25}\)

(xi) 2\(\frac{11}{100}\)

(xii) 898\(\frac{94}{125}\)

(xiii) 6\(\frac{27}{100}\)

(xiv) 252\(\frac{9}{20}\)

(xv) \(\frac{46}{125}\)

(xvi) 4\(\frac{8}{25}\)

(xvii) 52\(\frac{7}{20}\)

(xviii) 417\(\frac{1}{8}\)

(xix) 7\(\frac{123}{1000}\)

(xx) 15\(\frac{21}{100}\)

(xxi) 12\(\frac{17}{40}\)

(xxii) 151\(\frac{141}{1000}\)

(xxiii) 131\(\frac{41}{125}\)

(xxiv) 95\(\frac{171}{1000}\)

(xxv) 29\(\frac{6}{25}\)

(xxvi) 14\(\frac{3}{10}\)

(xxvii) 64\(\frac{1}{4}\)

(xxviii) 112\(\frac{8}{25}\)

(xxix) 46\(\frac{1}{200}\)

(xxx) 41\(\frac{11}{20}\)


4. Convert into fractions.

(i) 21.3

(ii) 0.26

(iii) 74.38

(iv) 48.25

(v) 0.008

(vi) 58.07

(vii) 1.03

(viii) 4.308

(ix) 73.003


Answer:

4. (i) \(\frac{213}{10}\)

(ii) \(\frac{26}{100}\)

(iii) \(\frac{7438}{100}\)

(iv) \(\frac{4825}{100}\)

(v) \(\frac{8}{1000}\)

(vi) \(\frac{5807}{100}\)

(vii) \(\frac{103}{100}\)

(viii) \(\frac{4308}{1000}\)

(ix) \(\frac{73003}{1000}\)

You might like these

Related Concept

Decimals

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number




7th Grade Math Problems

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