Conversion of Fractions to Decimal Numbers

We will discuss here about the working rule for the conversion of fractions to decimal numbers.

The rules for converting fractions with denominators 10, 100, 1000, etc. into decimal fraction:

(i) Count the number of zeroes coming after 1 in the denominator.

(ii) Count an equal number of places in the numerator starting from the unit digit then place the decimal point to the left of the digit reached.

Let us consider some of the following examples;

1. Convert 819/100 to decimal.

Given, 819/100

We see in 819/100 there are two zeroes in the denominator.

Therefore, to convert 819/100 into decimal fraction count two places from the right in the numerator and place the decimal point to the left of the digit.

= 8.19


2. Convert 6007/1000 to decimal.

Given, 6007/1000

We see in 6007/1000 there are three zeroes in the denominator.

Therefore, to convert 6007/1000 into decimal fraction count three places from the right in the numerator and place the decimal point to the left of the digit.

= 6.007


3. Convert 798/10000 to decimal.

Given, 798/10000

We see in 798/10000 there are four zeroes in the denominator.

Therefore, to convert 798/10000 into decimal fraction count four places from the right in the numerator and place the decimal point to the left of the digit.

= 0.0798


4. Convert 1794/10 to decimal.

Given, 1794/10

We see in 1794/10 there are one zero in the denominator.

Therefore, to convert 1794/10 into decimal fraction count one place from the right in the numerator and place the decimal point to the left of the digit.

= 179.4


5. Convert 8/100 to decimal.

Given, 8/100

= 0.08


6. Convert 3/10 to decimal.

Given, 3/10

= 0.3

7. Convert 5/1000 to decimal.

Given, 5/1000

= 0.005


8. Convert 9/10000 to decimal.

Given, 9/10000

= 0.0009


9. Convert 192/10 to decimal.

Given, 192/10

=19.2


10. Convert 94/1000 to decimal.

Given, 94/1000

= 0.094

Solved Examples on Fractions as Decimal

1. Express the following fractions as decimals.

(i) 23/10

(ii) 7/10

(iii) 44/1000

(iv) 367/1000

Solution:

(i) The given fraction is 23/10

There is one zero in the denominator of the given fraction 23/10

To convert the fraction 23/10 into decimals, count one place from the right in the numerator and place the decimal point to the left of the digit.

= 2.3

(ii) The given fraction is 7/10

There is one zero in the denominator of the given fraction 7/10

To convert the fraction 7/10 into decimals, count one place from the right in the numerator and place the decimal point to the left of the digit.

= 0.7

(iii) The given fraction is 44/1000

There is three zeros in the denominator of the given fraction 44/1000

To convert the fraction 44/1000 into decimals, count three places from the right in the numerator and place the decimal point to the left of the digit.

= 0.044

(iv) The given fraction is 367/1000

There is three zeros in the denominator of the given fraction 367/1000

To convert the fraction 367/1000 into decimals, count three places from the right in the numerator and place the decimal point to the left of the digit.

= 0.367

2. Express the following mixed fractions as decimals.

(i) 8\(\frac{2}{10}\)

(ii) 42\(\frac{3}{100}\)

(iii) 5\(\frac{4}{1000}\)

(iv) 4\(\frac{1}{100}\)

Solution:

(i) 8\(\frac{2}{10}\)

= \(\frac{8 × 10 + 2}{10}\)

= \(\frac{80 + 2}{10}\)

= \(\frac{82}{10}\)

= 8.2

(ii) 42\(\frac{3}{100}\)

= \(\frac{42 × 100 + 3}{100}\)

= \(\frac{4200 + 3}{100}\)

= \(\frac{4203}{100}\)

= 42.03

(iii) 5\(\frac{4}{1000}\)

= \(\frac{5 × 1000 + 4}{1000}\)

= \(\frac{5000 + 4}{1000}\)

= \(\frac{5004}{1000}\)

= 5.004

(iv) 4\(\frac{1}{100}\)

= \(\frac{4 × 100 + 1}{100}\)

= \(\frac{400 + 1}{100}\)

= \(\frac{401}{100}\)

= 4.01

Worksheet on Conversion of Fractions to Decimals Numbers

1. Express the following mixed numbers as decimals.

(i) 2\(\frac{1}{10}\)

(ii) 4\(\frac{7}{10}\)

(iii) 5\(\frac{3}{10}\)

(iv) 2\(\frac{7}{10}\)

(v) 4\(\frac{3}{100}\)

(vi) 37\(\frac{15}{100}\)

(vii) 95\(\frac{7}{100}\)

(viii) 105\(\frac{13}{100}\)

(ix) 7\(\frac{39}{1000}\)

(x) 85\(\frac{27}{1000}\)

(xi) 57\(\frac{3}{1000}\)

(xii) 81\(\frac{57}{1000}\)

Answer:

1. (i) 2.1

(ii) 4.7

(iii) 5.3

(iv) 2.7

(v) 4.03

(vi) 37.15

(vii) 95.07

(viii) 105.13

(ix) 7.039

(x) 85.027

(xi) 57.003

(xii) 81.057

2. Convert into decimal.

(i) \(\frac{1}{5}\)

(ii) \(\frac{3}{4}\)

(iii) \(\frac{3}{200}\)

(iv) \(\frac{9}{25}\)

(v) \(\frac{7}{50}\)

(vi) \(\frac{23}{250}\)

(vii) \(\frac{7}{8}\)

(viii) \(\frac{3}{40}\)

(ix) \(\frac{1}{4}\)

(x) 4\(\frac{1}{2}\)

(xi) 1\(\frac{1}{4}\)

(xii) 1\(\frac{4}{5}\)

(xiii) \(\frac{4}{25}\)

(xiv) \(\frac{21}{200}\)

(xv) 1\(\frac{3}{4}\)

(xvi) \(\frac{27}{50}\)

Answer:

2. (i) 0.2

(ii) 0.75

(iii) 0.015

(iv) 0.36

(v) 0.14

(vi) 0.092

(vii) 0.875

(viii) 0.075

(ix) 0.25

(x) 4.5

(xi) 1.25

(xii) 1.8

(xiii) 0.16

(xiv) 0.105

(xv) 1.75

(xvi) 0.54

● Decimal.

Decimal Place Value Chart.

Expanded form of Decimal Fractions.

Like Decimal Fractions.

Unlike Decimal Fraction.

Equivalent Decimal Fractions.

Changing Unlike to Like Decimal Fractions.

Ordering Decimals

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

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.

Simplification in Decimals.

Word Problems on Decimal.

5th Grade Numbers Page

5th Grade Math Problems

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