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Conversion of a Decimal Fraction into a Fractional Number
We will discuss here about the working rule for the conversion of a decimal fraction into a fractional number.
The rules of converting decimal number to fraction are:
(i) Write the given number leaving out the decimal point in the numerator.
(ii) Write 1 in the denominator followed by as many zeroes as the decimal places.
(iii) Then write the resulting fraction in the lowest form.
Let us consider some of the following example:
1. Convert 1.5 to fraction.
Given decimal fraction is 1.5.
To convert 1.5 into fractional number first we need to write in the numerator 15 leaving out the decimal point and then write 10 in the denominator since after the decimal point there is one number.
= 15/10
Now simplify 15/10 to its lowest form,
= 15/10 ÷ 5/5
= 3/2
2. Convert 21.72 to fraction.
Given decimal fraction is 21.72.
To convert 21.72 into fractional number first we need to write in the numerator 2172 leaving out the decimal point and then write 100 in the denominator since after the decimal point there is two numbers.
= 2172/100
Now simplify 2172/100 to its lowest form,
= 2172/100 ÷ 4/4
= 543/25
3. Convert 54.972 to fraction.
Given decimal fraction is 54.972.
To convert 54.972 into fractional number first we need to write in the numerator 54972 leaving out the decimal point and then write 1000 in the denominator since after the decimal point there is three numbers.
= 54972/1000
Now simplify 54972/1000 to its lowest form,
= 54972/1000÷ 4/4
= 13743/25
4. Convert 0.000893 to fraction.
Given decimal fraction is 0.000893.
To convert 0.000893 into fractional number first we need to write in the numerator 863 leaving out the decimal point and then write 1000000 in the denominator since after the decimal point there is three numbers.
= 863/1000000
[863/1000000 can’t reduce]
5. Convert 71.002 to fraction.
Given, 71.002
= 71002/1000
= 71002/1000 ÷ 2/2
= 35501/500
6. Convert 811.56 to fraction.
Given, 811.56
= 81156/100
= 81156/100 ÷ 4/4
= 20289/25
7. Convert 754.001 to fraction.
Given, 754.001
= 754001/1000
[754001/1000 can’t reduce]
8. Convert 1426.42 to fraction.
Given, 1426.42
= 142642/100
= 142642/100÷ 2/2
= 71321/50
9. Convert 100.1 to fraction.
Given, 100.1
= 1001/10
[1001/10 can’t reduce]
10. Convert 8364.64to fraction.
Given, 8364.64
= 836464/100
= 836464/100 ÷ 4/4
= 209116/25
11. Express the following decimals as mixed numbers or mixed fractions:
(i) 2.37
(ii) 4.83
Solution:
(i) 2.37
= 2 + \(\frac{3}{10}\) + \(\frac{7}{100}\)
= 2\(\frac{37}{100}\)
(i) 4.83
= 4 + \(\frac{8}{10}\) + \(\frac{3}{100}\)
= 4\(\frac{83}{100}\)
Worksheet on Conversion of a Decimal Fraction into a Fractional Number
1. Express the following decimals as mixed numbers.
(i) 1.37
(ii) 2.57
(iii) 7.37
(iv) 6.07
(v) 4.69
(vi) 7.038
(vii) 12.019
(viii) 17.328
(ix) 34.32
(x) 19.73
(xi) 14.72
(xii) 12.007
Answer:
1. (i) 1\(\frac{37}{100}\)
(ii) 2\(\frac{57}{100}\)
(iii) 7\(\frac{37}{100}\)
(iv) 6\(\frac{7}{100}\)
(v) 4\(\frac{69}{100}\)
(vi) 7\(\frac{38}{1000}\)
(vii) 12\(\frac{19}{1000}\)
(viii) 17\(\frac{328}{1000}\)
(ix) 34\(\frac{32}{100}\)
(x) 19\(\frac{73}{100}\)
(xi) 14\(\frac{72}{100}\)
(xii) 12\(\frac{7}{1000}\)
2. Convert the following decimals into fractions in its lowest terms:
(i) 7.35
(ii) 24.5
(iii) 6.25
(iv) 0.525
(v) 4.6
(vi) 21.06
(vii) 5.55
(viii) 9.425
(ix) 3.225
(x) 12.55
(xi) 1.025
(xii) 12.15
(xiii) 14.44
(xiv) 29.055
(xv) 5.321
(xvi) 11.035
Answer:
2. (i) \(\frac{147}{20}\)
(ii) \(\frac{49}{2}\)
(iii) \(\frac{25}{4}\)
(iv) \(\frac{21}{40}\)
(v) \(\frac{23}{5}\)
(vi) \(\frac{1053}{50}\)
(vii) \(\frac{111}{20}\)
(viii) \(\frac{377}{40}\)
(ix) \(\frac{129}{40}\)
(x) \(\frac{251}{20}\)
(xi) \(\frac{41}{40}\)
(xii) \(\frac{243}{20}\)
(xiii) \(\frac{361}{25}\)
(xiv) \(\frac{5811}{200}\)
(xv) \(\frac{5321}{1000}\)
(xvi) \(\frac{2207}{200}\)
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● Decimal.
Expanded form of Decimal Fractions.
Changing Unlike to Like Decimal Fractions.
Comparison of Decimal Fractions.
Conversion of a Decimal Fraction into a Fractional Number.
Conversion of Fractions to Decimals Numbers.
Addition of Decimal Fractions.
Problems on Addition of Decimal Fractions
Subtraction of Decimal Fractions.
Problems on Subtraction of Decimal Fractions
Multiplication of a Decimal Numbers.
Multiplication of a Decimal by a Decimal.
Properties of Multiplication of Decimal Numbers.
Problems on Multiplication of Decimal Fractions
Division of a Decimal by a Whole Number.
Division of Decimal Fractions by Multiples.
Division of a Decimal by a Decimal.
Division of a whole number by a Decimal.
Properties of Division of Decimal Numbers
Problems on Division of Decimal Fractions
Conversion of fraction to Decimal Fraction.
5th Grade Math Problems
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